Remarks on a multiplicity theorem for a perturbed Neumann problem

The aim of this article is to prove that, given two potential functionals Ψ₁, Ψ₂ on W1,2(Ω) which coincide on a set of the type , then under suitable summability conditions, certain local minima of Ψ₁ are local minima for Ψ₂ as well. An application of this result allows us to obtain a multiplicity theorem for a Neumann problem where we impose a less restrictive oscillating behavior on the nonlinearity than the one required in an analogous result recently established by B. Ricceri.     

Existence and multiplicity of solutions to a perturbed Neumann problem

In this paper we establish an existence theorem of strong solutions to a perturbed Neumann problem of the type In particular, our solutions take their values in a fixed real interval. This latter fact allows us to state a multiplicity result assuming on f an oscillating behavior. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Neumann problem for elliptic equations involving the p-Laplacian

The aim of this paper is to establish the existence of an unbounded sequence of weak solutions to a Neumann problem for elliptic equations involving the p-Laplacian.     

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.      

Existence and multiplicity for solutions of Neumann problem for semilinear elliptic equations

The existence and multiplicity results are obtained for solutions of Neumann problem for semilinear elliptic equations by the least action principle and the minimax methods respectively.     

On a critical Neumann problem with a perturbation of lower order

We investigate the solvability of the Neumann problem （1.1） involving the critical Sobolev nonlinearity and a term of lower order. We allow a coefficient of u in equation （1.1） to be unbounded. We prove the existence of a solution in a weighted Sobolev space.     

On the nonlinear Neumann problem involving the critical Sobolev exponent on the boundary

In this paper we investigate the solvability of the Neumann problem (1.1) involving the critical Sobolev exponents on the right-hand side of the equation and in the boundary condition. It is assumed that the coefficients Q and P are smooth. We examine the common effect of the mean curvature of the boundary ∂Ω and the shape of the graph of the coefficients Q and P on the existence of solutions of problem (1.1).     

The critical Neumann problem for semilinear elliptic equations with concave perturbations

We consider the semilinear Neumann problem involving the critical Sobolev exponent with an indefinite weight function and a concave purturbation. We prove the existence of two distinct solutions.      

Multiplicity results for a Neumann problem involving the p-Laplacian

In this paper, we establish some multiplicity results for the following Neumann problem:

     

The Neumann problem for some degenerate elliptic equations

In the paper we study the equation L _u = f, where L is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set μ. We prove existence and uniqueness of solutions in the space H(μ) for the Neumann problem.     

On the high multiplicity traveling salesman problem

This paper considers a version of the traveling salesman problem where the cities are to be visited multiple times. Each city has its own required number of visits. We investigate how the optimal solution and its objective value change when the numbers of visits are increased by a common multiplicator. In addition, we derive lower bounds on values of the multiplicator beyond which further increase does not improve the average tour length. Moreover, we show how and when the structure of an optimal tour length can be derived from tours with smaller multiplicities.     

Solvability of the Neumann problem for a Sobolev pseudoparabolic equation

The dynamic potential constructed in this paper is used to analyze the existence of a classical solution to the Neumann problem for a Sobolev equation.     

Existence of positive solutions of superlinear second-order Neumann boundary value problem

In this paper, we consider the Neumann boundary value problem

     

Uniqueness of the least-energy solution for a semilinear Neumann problem

We prove that the least-energy solution of the problem

where is a ball, and if , if , is unique (up to rotation) if is small enough.

     

Neumann problem for generalized n-Poisson equation

Using a hierarchy of integral operators having higher-order Neumann functions and their derivatives as kernels, the Neumann problem for a 2nth order linear partial complex differential equation is discussed. The solvability of the problem is obtained.     

Existence of multiple positive solutions for inhomogeneous Neumann problem

In this paper, we study the existence and nonexistence of multiple positive solutions for the inhomogeneous Neumann boundary value problem

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