R~N上的Kirchhoff {-型问题非平凡解的存在性和多解性

考虑如下Kirchhoff型问题{-(a+b∫RN︱▽u︱2dx)△u+V(x)u=f(x,u)u∈H1(RN)在RN上,通过山路引理,喷泉定理和对称山路引理得到问题非平凡解的存在性和多解性.     

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL

In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well■ in R³,where a,b> 0 are constants,λ is a positive parameter,V ∈ C(R³,R) is a steep potential well and the nonlinearity f ∈ C(R,R) satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)_C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains w...     

含有陡峭势阱和凹凸非线性项的Kirchhoff型问题的多重正解*

在这篇文章中, 作者研究涉及凹凸非线性项的Kirchhoff型问题-(a + b ∫R3|▽u|²dx) Δu + λV (x)u = μf(x)|u|^q?2u + |u|^p?2u, x ∈ R³,u ∈ H¹(R³),其中a,b > 0 是常数, λ, μ > 0 是参数, 1 < q < 2, 4 < p < 6 且 V 是一个非负连续位势. 在f(x) 和 V 的合适条件下,此问题正解的存在性和集中性能够通过Nehari 流形和Ekeland 变分原理得到.     

HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS

The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t)+▽V(t,q(t))=0,where V(t,x)=-K(t,x)+W(t,x),K(t,x) is neither a quadratic form in x nor periodic in t and W(t,x) is superquadratic in x.     

自反Banach空间上的半强制单调变分问题

仅用变分法的经典定理，研究了自反Ｂａｎａｃｈ空间上的半强制单调变分问题．获得了自反Ｂａｎａｃｈ空间上半线性方程解的存在性     

AN EXISTENCE THEOREM OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS ON R~N

1991MRSubjectClassification35C15,58E50ConsiderthesernilinearellipticdifferentialequationInthestudyofllollliliearSchrodingerequations,nonlinearequationsofKleili~Gordolltypeall(1reaction-diffusiollequatiolls,sollltionsof(1)correspolldtostalldingwavesolutions.stroll(lill~(ortraveling)wavesolutionsandsteadystatesofthesystem.Manypapersdealtwiththeautonomouscasewhere5andfareindependentofatorwiththeradiallysynlluetriccasewherebandfdependonfi](see[1-4]andtheirreferences).Recentlytheperiodiccaseand…     

Multiplicity of positive solutions for a class of concave-convex elliptic equations with critical growth

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∈■Ω where Ω■R~N(N≥3) is an open bounded domain with smooth boundary, 1 q 2, λ 0.2*=2 N/(N-2)is the critical Sobolev exponent,f∈L2~*/(2~*-q)(Ω)is nonzero and nonnegative,and g ∈ C(■) 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) 2660-2671].     

PERTURBATION METHODS IN SEMILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENT

In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory.     

具有Hardy奇异项的共振半线性椭圆方程的解

利用变分法研究了具有Dirichlet边值问题-△u-μ(u/(|x|²))=f(x,u)的解的存在性问题,在适当的条件下给出了其解的存在性定理.