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
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
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
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.
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.
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.
