On exterior Neumann problems with an asymptotically linear nonlinearity

In this paper, we study exterior Neumann problems with an asymptotically linear nonlinearity. We establish the existence of ground state solutions. Furthermore when the domain is a complement of a ball, we prove the ground state solutions are not radially symmetric. We also give asymptotic profiles of ground state solutions.     

Nontrivial periodic solutions for asymptotically linear resonant difference problem

In this paper the existence of nontrivial periodic solution for second order asymptotically linear difference equation at resonance is obtained. The methods used here are based on combining the minimax methods and the Morse theory, especially the observation on the critical groups.     

Nonnegative solutions of elliptic problems with sublinear indefinite nonlinearity

We are concerned with existence, nonexistence and multiplicity of nonnegative solutions for the elliptic problem

     

Positive solutions for Neumann problems with indefinite and unbounded potential

We consider semilinear Neumann equations with an indefinite and unbounded potential. We establish the existence and uniqueness of positive solutions. We show that our setting incorporates as special cases several parametric equations of interest (such as the equidiffusive logistic equation).     

一类渐近线性Neumann问题正解的存在性

利用变分法获得了一类渐近线性N eum ann问题正解的存在性结果.     

Local superlinearity and sublinearity for indefinite semilinear elliptic problems

In this paper the usual notions of superlinearity and sublinearity for semilinear problems like −Δu=f(x,u) are given a local form and extended to indefinite nonlinearities. Here f(x,s) is allowed to change sign or to vanish for s near zero as well as for s near infinity. Some of the well-known results of Ambrosetti-Brézis-Cerami are partially extended to this context.     

Local existence of solutions for the Neumann problem of the nonlinear elastodynamic system outside a domain

In this paper, we study the mixed initial-boundary value problem of Neumann type for the nonlinear elastic wave equation outside a domain. The local existence of solutions to this problem is proved by iteration. To get this result, we prove the existence of solutions for the second order linear hyperbolic system with variable coefficients (in Sobolev spaces) outside of a domain by using linear evolution operators and integro-differential equations.     

Neumann problems with resonance in the first eigenvalue

The aim of this work is to present results of existence of solutions for a class of superlinear asymmetric elliptic systems with resonance in the first eigenvalue. The asymmetry that we consider has linear behavior on and superlinear on . To obtain these results we apply topological degree theory.     

Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.     

一类二阶离散Neumann边值问题正解的存在性

研究一类二阶离散Neumann边值问题正解的存在性,运用不动点指数理论获得了方程存在正解的最优条件,并给出一个具体例子说明这一结果。     

On eigenvalue problems with Robin type boundary conditions having indefinite coefficients

A Robin type boundary condition with a sign-changing coefficient is treated. First, the associated linear elliptic eigenvalue problem is studied, where the existence of a principal eigenvalue is discussed by the use of a variational approach. Second, the associated semilinear elliptic boundary value problem of logistic type is studied and the one parameter-dependent structure of positive solutions is investigated, where results obtained are due to the construction of suitable super- and subsolutions by using the principal positive eigenfunctions of the linear eigenvalue problem.     

Existence of multiple solutions with precise sign information for superlinear Neumann problems

We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator and having a p-superlinear nonlinearity. Using truncation techniques combined with the method of upper–lower solutions and variational arguments based on critical point theory, we prove the existence of five nontrivial smooth solutions, two positive, two negative and one nodal. For the semilinear (i.e., p = 2) problem, using critical groups we produce a second nodal solution. This paper was completed while N.S. Papageorgiou was visiting the University of Aveiro as an invited scientist. The hospitality and financial support of the host institution are gratefully acknowledged. V. Staicu acknowledges partial financial support from the Portuguese Foundation for Sciences and Technology (FCT) under the project POCI/MAT/55524/2004.     

Multiple positive solutions of nonlinear Neumann problems with time and space singularities

Allowing the nonlinear term to be singular with respect to both the time and space variables, we consider the positive solutions of a nonlinear Neumann boundary value problem. By constructing two height functions and estimating the integrations of these height functions, the existence and multiplicity of positive solutions are established.     

Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities

We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (Il), l>2 and (IIl), l?1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions.     

Spike-layered solutions for an elliptic system with Neumann boundary conditions

We prove the existence of nonconstant positive solutions for a system of the form , in , with Neumann boundary conditions on , where is a smooth bounded domain and , are power-type nonlinearities having superlinear and subcritical growth at infinity. For small values of , the corresponding solutions and admit a unique maximum point which is located at the boundary of .

     

A multiplicity theorem for the Neumann p-Laplacian with an asymmetric nonsmooth potential

We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequality). By combining variational with degree theoretic techniques, we prove a multiplicity theorem. In the process, we also prove a result of independent interest relating and local minimizers, of a nonsmooth locally Lipschitz functional.      

Critical groups at infinity for p-Laplacian equations with indefinite nonlinearities

In this paper, by a kind of decomposition lemma and Künneth formula we study the critical groups at infinity for the associated functional of the following p-Laplacian equation with indefinite nonlinearities

     

Multiple existence of solutions for a semilinear elliptic problem with Neumann boundary condition

The multiplicity of solutions for semilinear elliptic equations with exponential growth nonlinearities is treated. The approach to the problem is a variational method.