The Toda system and multiple-end solutions of autonomous planar elliptic problems

We prove the existence of a new class of entire, positive solutions for the classical elliptic problem Δu−u+up=0 in R², when p>2. The solutions we construct are obtained by perturbing the function

     

Uniqueness of solutions for a mean field equation on torus

We consider on a two-dimensional flat torus T the following equation

     

High-energy solutions for a phase transition problem

In this article we study the existence and profile of high-energy solutions for the phase transition model

     

Multiple fixed-sign solutions for a system of generalized right focal problems with deviating arguments

We consider the following system of generalized right focal boundary value problems

     

Periodic solutions for the 1-dimensional p-Laplacian equation

Existence of infinitely many periodic solutions for the 1-dimensional p-Laplacian equation

     

Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions

We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space Hβ,1 with for the nonlinear Klein-Gordon equation with a power nonlinearity

     

On a class of nonlinear elliptic equations with fast increasing weight and critical growth

We are concerned with the existence of rapidly decaying solutions for the equation

     

Singular quasilinear equations with quadratic growth in the gradient without sign condition

Given a bounded domain Ω in RN, and a function a∈Lq(Ω) with q>N/2, we study the existence of a positive solution for the quasilinear problem

     

Positive solutions to sublinear second-order divergence type elliptic equations in cone-like domains

We study the existence and nonexistence of positive solutions to a sublinear (p<1) second-order divergence type elliptic equation in unbounded cone-like domains CΩ. We prove the existence of the critical exponent

     

Existence and nonexistence of least energy solutions of the Neumann problem for a semilinear elliptic equation with critical Sobolev exponent and a critical lower-order perturbation

Let Ω be a smooth bounded domain in , with N?5, a>0, α?0 and . We show that the exponent plays a critical role regarding the existence of least energy (or ground state) solutions of the Neumann problem

     

Irregular scaling functions with orthogonal translations

For all integers m,k>1 with m≡1modk we construct, among others, a function with dense graph in the set [0,k]×R such that

     

Solvability of the resonant 1-dimensional periodic p-Laplacian equations

In this paper we study the existence of 2π-periodic solutions of

     

Existence of periodic solutions for a 2nth-order nonlinear difference equation

The authors consider the 2nth-order difference equation

     

On the structure of global solutions of the nonlinear heat equation in a ball

In this paper, we consider the nonlinear heat equation

(NLH)

u_t−Δu=|u|^αu,