In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative tech...In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative technique.展开更多
In this paper we will be concerned with the problem -ΔU-1/2Δ(a(x)u^(2))u+v(x)u=f(u),x∈R^(2),where V is a potential continuous and f:R→R is a superlinear continuous function with exponential subcritical or exponent...In this paper we will be concerned with the problem -ΔU-1/2Δ(a(x)u^(2))u+v(x)u=f(u),x∈R^(2),where V is a potential continuous and f:R→R is a superlinear continuous function with exponential subcritical or exponential critical growth.We use as a main tool the Nehari manifold method in order to show existence of nonnegative solutions and existence of nodal solutions.Our results complement the classical result of“Solutions for quasilinear Schrdinger equations via the Nehari method”due to Jia–Quan Liu,Ya–Qi Wang and Zhi-Qiang Wang in the sense that in this article we are considering nonlinearity of the exponential type.展开更多
In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an op...In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an open bounded domain with smooth boundary, 1 〈 q 〈 2, λ 〉 0. 2＊= 2N/N-2 is the critical Sobolev exponent, f ∈L2＊/2N/N-2 is nonzero and nonnegative, and g E （Ω） is a positive function with k local maximum points. By the Nehari method and variational method, k ＋ 1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75（2012） 2660-26711.展开更多
Using Nehari manifold method combined with fibring maps,we show the existence of nontrivial,weak,positive solutions of the nonlinear y-Riemann-Liouville fractional boundary value problem involving the p-Laplacian oper...Using Nehari manifold method combined with fibring maps,we show the existence of nontrivial,weak,positive solutions of the nonlinear y-Riemann-Liouville fractional boundary value problem involving the p-Laplacian operator,given by(P){-t^(D)_(T)(|_(0)(D)_(T)^(a,ψ)(u(t))|_(0)^(p-2)D_(t)^(a,ψ)(u(t)))=λg(t)/uγ(t)+f(t,u(t)),t∈(0,T),u(0)=u(T)=0,where l>0,0<g<1<p and 1/p<a≤1,g2C([0,T])and f 2C1([0,T]×R,R)A useful examples are presented in order to illustrate the validity of our main results.展开更多
文摘In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative technique.
文摘In this paper we will be concerned with the problem -ΔU-1/2Δ(a(x)u^(2))u+v(x)u=f(u),x∈R^(2),where V is a potential continuous and f:R→R is a superlinear continuous function with exponential subcritical or exponential critical growth.We use as a main tool the Nehari manifold method in order to show existence of nonnegative solutions and existence of nodal solutions.Our results complement the classical result of“Solutions for quasilinear Schrdinger equations via the Nehari method”due to Jia–Quan Liu,Ya–Qi Wang and Zhi-Qiang Wang in the sense that in this article we are considering nonlinearity of the exponential type.
基金Supported by National Natural Science Foundation of China(11471267)the Doctoral Scientific Research Funds of China West Normal University(15D006 and 16E014)+1 种基金Meritocracy Research Funds of China West Normal University(17YC383)Natural Science Foundation of Education of Guizhou Province(KY[2016]046)
文摘In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g（x）｜u｜2＊-2u＋λf（x）｜u｜q-2u,x∈Ω u=0,x∈δΩ where Ω RN（N ≥ 3） is an open bounded domain with smooth boundary, 1 〈 q 〈 2, λ 〉 0. 2＊= 2N/N-2 is the critical Sobolev exponent, f ∈L2＊/2N/N-2 is nonzero and nonnegative, and g E （Ω） is a positive function with k local maximum points. By the Nehari method and variational method, k ＋ 1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75（2012） 2660-26711.
文摘Using Nehari manifold method combined with fibring maps,we show the existence of nontrivial,weak,positive solutions of the nonlinear y-Riemann-Liouville fractional boundary value problem involving the p-Laplacian operator,given by(P){-t^(D)_(T)(|_(0)(D)_(T)^(a,ψ)(u(t))|_(0)^(p-2)D_(t)^(a,ψ)(u(t)))=λg(t)/uγ(t)+f(t,u(t)),t∈(0,T),u(0)=u(T)=0,where l>0,0<g<1<p and 1/p<a≤1,g2C([0,T])and f 2C1([0,T]×R,R)A useful examples are presented in order to illustrate the validity of our main results.
