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
We consider the nonlinear difference equations of the form Lu=f（n,u）,n∈Z,where L is a Jacobi operator given by（Lu）（n）=a（n）u（n＋1）＋a（n-1）u（n-1）＋b（n）u（n） for n ∈Z,{a（n）} and {b（n）} are real val...We consider the nonlinear difference equations of the form Lu=f（n,u）,n∈Z,where L is a Jacobi operator given by（Lu）（n）=a（n）u（n＋1）＋a（n-1）u（n-1）＋b（n）u（n） for n ∈Z,{a（n）} and {b（n）} are real valued N-periodic sequences,and f（n,t） is superlinear on t.Inspired by previous work of Pankov[Discrete Contin.Dyn.Syst.,19,419-430（2007）]and Szulkin and Weth[J.Funct.Anal.,257,3802-3822（2009）],we develop a non-Nehari manifold method to find ground state solutions of Nehari-Pankov type under weaker conditions on f.Unlike the Nehari manifold method,the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.展开更多
In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence o...In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence of multiple nontrivial nonnegative solutions to this equation is verified.展开更多
We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in R^N . We relate the number of positive solutions to the topology of...We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in R^N . We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.展开更多
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 NSFC(Grant No.11571370)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20120162110021)of China
文摘We consider the nonlinear difference equations of the form Lu=f（n,u）,n∈Z,where L is a Jacobi operator given by（Lu）（n）=a（n）u（n＋1）＋a（n-1）u（n-1）＋b（n）u（n） for n ∈Z,{a（n）} and {b（n）} are real valued N-periodic sequences,and f（n,t） is superlinear on t.Inspired by previous work of Pankov[Discrete Contin.Dyn.Syst.,19,419-430（2007）]and Szulkin and Weth[J.Funct.Anal.,257,3802-3822（2009）],we develop a non-Nehari manifold method to find ground state solutions of Nehari-Pankov type under weaker conditions on f.Unlike the Nehari manifold method,the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.
文摘In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence of multiple nontrivial nonnegative solutions to this equation is verified.
基金Supported by CAS-KJCX3-SYW-S03,Grant Fondecyt No. 1050613Scientific Research Fund for Youth of Hubei Provincial Education Department(Q20083401)
文摘We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in R^N . We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.
