This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation b...This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.展开更多
In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/...In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.展开更多
In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence ...In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.展开更多
We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical ...We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical Sobolev exponent in 1R3.Under some more general assumptions on f,we prove that(0.1)admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.展开更多
This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solution...This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.展开更多
We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of...We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of nonnegative ground state solutions is established.Our method relies upon the variational method and some analysis tricks.展开更多
We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under som...We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.展开更多
In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a posit...In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a positive global minimum,and K∈C(R^N)∩L∞(R^N)has a positive global maximum.By using a change of variable,we obtain the existence and concentration behavior of ground state solutions for this problem and establish a phenomenon of exponential decay.展开更多
In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,...In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,κ∂_(1)A_(0)=e^(2)A_(2)u^(2),κ∂_(2)A_(0)=−e^(2)A_(1)u^(2),where u∈H^(1)(R^(2)),p∈(2,4),Aα:R^(2)→R are the components of the gauge potential(α=0,1,2),N:R^(2)→R is a neutral scalar field,V(x)is a potential function,the parametersκ,q>0 represent the Chern-Simons coupling constant and the Maxwell coupling constant,respectively,and e>0 is the coupling constant.In this paper,the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem.The ground state solution of the problem(P)is obtained by using the variational method.展开更多
This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. ...This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature.展开更多
This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We stud...This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.展开更多
In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger...In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.展开更多
In this paper,we study the following coupled nonlinear logarithmic Hartree system{-Δu+λ_(1)u=μ_(1)(-1/2πln|x|*u^(2))u+β(-1/2πln|x|*v^(2))u,x∈R^(2),-Δv+λ_(2)v=μ_(2)(-1/2πln|x|*v^(2))v+β(-1/2πln|x|*u^(2))v,...In this paper,we study the following coupled nonlinear logarithmic Hartree system{-Δu+λ_(1)u=μ_(1)(-1/2πln|x|*u^(2))u+β(-1/2πln|x|*v^(2))u,x∈R^(2),-Δv+λ_(2)v=μ_(2)(-1/2πln|x|*v^(2))v+β(-1/2πln|x|*u^(2))v,x∈R^(2),where β,μ_(i),λ_(i)(i=1,2)are positive constants,* denotes the convolution in R^(2).By considering the constraint minimum problem on the Nehari manifold,we prove the existence of ground state solutions for β>0 large enough.Moreover,we also show that every positive solution is radially symmetric and decays exponentially.展开更多
We consider the following Schrodinger-Newton system with negative critical nonlocal term where a and f satisfy some certain conditions.By using the variational method and analytical techniques,we obtain the existence ...We consider the following Schrodinger-Newton system with negative critical nonlocal term where a and f satisfy some certain conditions.By using the variational method and analytical techniques,we obtain the existence of positive ground state solutions which improves the recent results in the literature.展开更多
We investigate the Kirchhoff type elliptic problem(a+b∫_(R^(N))[|∇u|^(2)+V(x)u^(2)]dx)[-Δu+V(x)u]=f(x,u),x∈R^(N),where both V and f are periodic in x,0 belongs to a spectral gap of−∆+V.Under suitable assumptions on...We investigate the Kirchhoff type elliptic problem(a+b∫_(R^(N))[|∇u|^(2)+V(x)u^(2)]dx)[-Δu+V(x)u]=f(x,u),x∈R^(N),where both V and f are periodic in x,0 belongs to a spectral gap of−∆+V.Under suitable assumptions on V and f with more general conditions,we prove the existence of ground state solutions and infinitely many geometrically distinct solutions.展开更多
In this paper,the authors consider the following singular Kirchhoff-Schrodinger problem M(∫_(R^(N))|∇u|^(N)+V(x)|u|^(N)dx)(−Δ_(N)u+V(x)|u|^(N-2)u)=f(x,u)/|x|^(η)in R^(N),(P_(η))where 0<η<N,M is a Kirchhoff-...In this paper,the authors consider the following singular Kirchhoff-Schrodinger problem M(∫_(R^(N))|∇u|^(N)+V(x)|u|^(N)dx)(−Δ_(N)u+V(x)|u|^(N-2)u)=f(x,u)/|x|^(η)in R^(N),(P_(η))where 0<η<N,M is a Kirchhoff-type function and V(x)is a continuous function with positive lower bound,f(x,t)has a critical exponential growth behavior at infinity.Combining variational techniques with some estimates,they get the existence of ground state solution for(P_(η)).Moreover,they also get the same result without the A-R condition.展开更多
We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the ...We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold.展开更多
We consider the following quasilinear Schrodinger equation involving p-Laplacian-Δpu+V(x)|u|^(p-2)u-Δp(|u|^(2η))|u|^(2η-2)u=λ|u|^(q-2)u/|x|^(μ)+|u|^(2ηp*(v)-2)u/|x|^(v)in R^(N),where N>p>1,η≥p/2(p-1),p&...We consider the following quasilinear Schrodinger equation involving p-Laplacian-Δpu+V(x)|u|^(p-2)u-Δp(|u|^(2η))|u|^(2η-2)u=λ|u|^(q-2)u/|x|^(μ)+|u|^(2ηp*(v)-2)u/|x|^(v)in R^(N),where N>p>1,η≥p/2(p-1),p<q<2ηp^(*)(μ),p^(*)(s)=(p(N-s))/N-p,andλ,μ,νare parameters withλ>0,μ,ν∈[0,p).Via the Mountain Pass Theorem and the Concentration Compactness Principle,we establish the existence of nontrivial ground state solutions for the above problem.展开更多
In this paper,we are concerned with the autonomous Choquard equation−Δu+u=(Iα∗|u|^(α/N+1))|u|^(α/N−1)u+|u|^(2∗−2)u+f(u)inR^(N),where N≥3,Iαdenotes the Riesz potential of orderα∈(0,N),the exponentsα/N+1 and 2^...In this paper,we are concerned with the autonomous Choquard equation−Δu+u=(Iα∗|u|^(α/N+1))|u|^(α/N−1)u+|u|^(2∗−2)u+f(u)inR^(N),where N≥3,Iαdenotes the Riesz potential of orderα∈(0,N),the exponentsα/N+1 and 2^(∗)=2N/(N−2)are critical with respect to the Hardy-Littlewood-Sobolev inequality and Sobolev embedding,respectively.Based on the variational methods,by using the minimax principles and the Pohožaev manifold method,we prove the existence of ground state solution under some suitable assumptions on the perturbation f.展开更多
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
基金Supported by Research Start-up Fund of Jianghan University(06050001).
文摘This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.
基金Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236)Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)National Natural Science Foundation of China Youth Foud of China Youth Foud(Grant No.12101192).
文摘In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.
基金supported by National Natural Science Foundation of China(11971393)。
文摘In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.
基金the Science and Technology Project of Education Department in Jiangxi Province(GJJ180357)the second author was supported by NSFC(11701178).
文摘We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical Sobolev exponent in 1R3.Under some more general assumptions on f,we prove that(0.1)admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.
基金supported by the Hunan Provincial Innovation Foundation for Postgraduate(CX2013A003)the NNSF(11171351,11361078)SRFDP(20120162110021)of China
文摘This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.
基金National Natural Science Foundation of China(11471267)the first author was supported by Graduate Student Scientific Research Innovation Projects of Chongqing(CYS17084).
文摘We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of nonnegative ground state solutions is established.Our method relies upon the variational method and some analysis tricks.
基金supported by National Natural Science Foundation of China(11971202)Outstanding Young foundation of Jiangsu Province(BK20200042)。
文摘We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.
基金supported by the National Natural Science Foundation of China(11661053,11771198,11901345,11901276,11961045 and 11971485)partly by the Provincial Natural Science Foundation of Jiangxi,China(20161BAB201009 and 20181BAB201003)+1 种基金the Outstanding Youth Scientist Foundation Plan of Jiangxi(20171BCB23004)the Yunnan Local Colleges Applied Basic Research Projects(2017FH001-011).
文摘In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a positive global minimum,and K∈C(R^N)∩L∞(R^N)has a positive global maximum.By using a change of variable,we obtain the existence and concentration behavior of ground state solutions for this problem and establish a phenomenon of exponential decay.
基金partially supported by NSFC (12161044)Natural Science Foundation of Jiangxi Province (20212BAB211013)+1 种基金Benniao Li was partially supported by NSFC (12101274)Doctoral Research Startup Foundation of Jiangxi Normal University (12020927)
文摘In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,κ∂_(1)A_(0)=e^(2)A_(2)u^(2),κ∂_(2)A_(0)=−e^(2)A_(1)u^(2),where u∈H^(1)(R^(2)),p∈(2,4),Aα:R^(2)→R are the components of the gauge potential(α=0,1,2),N:R^(2)→R is a neutral scalar field,V(x)is a potential function,the parametersκ,q>0 represent the Chern-Simons coupling constant and the Maxwell coupling constant,respectively,and e>0 is the coupling constant.In this paper,the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem.The ground state solution of the problem(P)is obtained by using the variational method.
文摘This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature.
文摘This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.
文摘In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.
基金partially supported by the Natural Science Foundation of China(Grant No.12061012)the special foundation for Guangxi Ba Gui Scholars.
文摘In this paper,we study the following coupled nonlinear logarithmic Hartree system{-Δu+λ_(1)u=μ_(1)(-1/2πln|x|*u^(2))u+β(-1/2πln|x|*v^(2))u,x∈R^(2),-Δv+λ_(2)v=μ_(2)(-1/2πln|x|*v^(2))v+β(-1/2πln|x|*u^(2))v,x∈R^(2),where β,μ_(i),λ_(i)(i=1,2)are positive constants,* denotes the convolution in R^(2).By considering the constraint minimum problem on the Nehari manifold,we prove the existence of ground state solutions for β>0 large enough.Moreover,we also show that every positive solution is radially symmetric and decays exponentially.
文摘We consider the following Schrodinger-Newton system with negative critical nonlocal term where a and f satisfy some certain conditions.By using the variational method and analytical techniques,we obtain the existence of positive ground state solutions which improves the recent results in the literature.
基金supported by Natural Science Foundation of Fujian Province(Nos.2022J01339 and 2020J01708)National Foundation Training Program of Jimei University(ZP2020057)。
文摘We investigate the Kirchhoff type elliptic problem(a+b∫_(R^(N))[|∇u|^(2)+V(x)u^(2)]dx)[-Δu+V(x)u]=f(x,u),x∈R^(N),where both V and f are periodic in x,0 belongs to a spectral gap of−∆+V.Under suitable assumptions on V and f with more general conditions,we prove the existence of ground state solutions and infinitely many geometrically distinct solutions.
基金supported by the National Natural Science Foundation of China(Nos.11790271,12171108,12201089)Guangdong Basic and Applied basic Research Foundation(No.2020A1515011019)Innovation and Development Project of Guangzhou University and Chongqing Normal University Foundation(No.21XLB039)。
文摘In this paper,the authors consider the following singular Kirchhoff-Schrodinger problem M(∫_(R^(N))|∇u|^(N)+V(x)|u|^(N)dx)(−Δ_(N)u+V(x)|u|^(N-2)u)=f(x,u)/|x|^(η)in R^(N),(P_(η))where 0<η<N,M is a Kirchhoff-type function and V(x)is a continuous function with positive lower bound,f(x,t)has a critical exponential growth behavior at infinity.Combining variational techniques with some estimates,they get the existence of ground state solution for(P_(η)).Moreover,they also get the same result without the A-R condition.
基金supportedby the National Natural Science Foundation of China(Grant No.11971393).
文摘We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold.
基金supported by the National Natural Science Foundation of China (12226411)the Research Ability Cultivation Fund of HUAS (No.2020kypytd006)+1 种基金supported by the National Natural Science Foundation of China (11931012,11871386)the Fundamental Research Funds for the Central Universities (WUT:2020IB019)。
文摘We consider the following quasilinear Schrodinger equation involving p-Laplacian-Δpu+V(x)|u|^(p-2)u-Δp(|u|^(2η))|u|^(2η-2)u=λ|u|^(q-2)u/|x|^(μ)+|u|^(2ηp*(v)-2)u/|x|^(v)in R^(N),where N>p>1,η≥p/2(p-1),p<q<2ηp^(*)(μ),p^(*)(s)=(p(N-s))/N-p,andλ,μ,νare parameters withλ>0,μ,ν∈[0,p).Via the Mountain Pass Theorem and the Concentration Compactness Principle,we establish the existence of nontrivial ground state solutions for the above problem.
基金This paper is supported by the National Natural Science Foundation of China(No.11971393).
文摘In this paper,we are concerned with the autonomous Choquard equation−Δu+u=(Iα∗|u|^(α/N+1))|u|^(α/N−1)u+|u|^(2∗−2)u+f(u)inR^(N),where N≥3,Iαdenotes the Riesz potential of orderα∈(0,N),the exponentsα/N+1 and 2^(∗)=2N/(N−2)are critical with respect to the Hardy-Littlewood-Sobolev inequality and Sobolev embedding,respectively.Based on the variational methods,by using the minimax principles and the Pohožaev manifold method,we prove the existence of ground state solution under some suitable assumptions on the perturbation f.
