We investigate the radial symmetry of minimizers on the Pohozaev-Nehari manifold to the Schrodinger Poisson equation with a general nonlinearity f(u).Particularly,we allow that f is L^(2) supercritical.The main result...We investigate the radial symmetry of minimizers on the Pohozaev-Nehari manifold to the Schrodinger Poisson equation with a general nonlinearity f(u).Particularly,we allow that f is L^(2) supercritical.The main result shows that minimizers are radially symmetric modulo suitable translations.展开更多
In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Und...In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution.展开更多
In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parame...In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parameter,■ , and V : R^3→ R is a continuous potential function. For suitable assumptions on V, we show the existence of a positive ground state solution, by using the methods of the Pohozaev-Nehari manifold, Jeanjean's monotonicity trick and the concentration-compactness principle due to Lions(1984).展开更多
The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equat...The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1, 2 and they can be stable for N ≥ 3 for suitable values of the involved exponents.展开更多
基金supported by the NSFC(12031015)Song's research was supported by the Shuimu Tsinghua Scholar Program,the National Funded Postdoctoral Research Program(GZB20230368)the China Postdoctoral Science Foundation(2024T170452)。
文摘We investigate the radial symmetry of minimizers on the Pohozaev-Nehari manifold to the Schrodinger Poisson equation with a general nonlinearity f(u).Particularly,we allow that f is L^(2) supercritical.The main result shows that minimizers are radially symmetric modulo suitable translations.
基金Supported by NSFC(No.12561023)partly by the Provincial Natural Science Foundation of Jiangxi,China(Nos.20232BAB201001,20202BAB211004)。
文摘In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution.
基金supported by National Natural Science Foundation of China (Grant Nos. 11771468 and 11271386)supported by National Natural Science Foundation of China (Grant Nos. 11771234 and 11371212)
文摘In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parameter,■ , and V : R^3→ R is a continuous potential function. For suitable assumptions on V, we show the existence of a positive ground state solution, by using the methods of the Pohozaev-Nehari manifold, Jeanjean's monotonicity trick and the concentration-compactness principle due to Lions(1984).
基金supported by the projects of the DGISPI(Spain)(Ref.MTM2011-26119,MTM2014-57113)the UCM Research Group MOMAT(Ref.910480)
文摘The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1, 2 and they can be stable for N ≥ 3 for suitable values of the involved exponents.
