Ederson Moreira dos Santos

Ground state and non-ground state solutions of some strongly coupled elliptic systems

We study an elliptic system of the form Lu = ⌊v⌋p&1 v and Lv = ⌊u⌋ q&1 u in Ω with homogeneous Dirichlet boundary condition, where Lu:= &Δu in the case of a bounded domain and Lu:= &Δu + u in the cases of an exterior domain or the whole space RN. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

Hamiltonian elliptic systems: a guide to variational frameworks

Consider a Hamiltonian elliptic system of type 8 < : u = Hv(u;v) in v = Hu(u;v) in u;v = 0 on @ where H is a power-type nonlinearity, for instance H(u;v) =juj p+1 =(p + 1) +jvj q+1 =(q + 1); having subcritical growth, and is a bounded domain of R N , N 1. The aim of this paper is to give an overview of the several variational frameworks that can be used to treat such a system. Within each approach, we address existence of solutions, and in particular of ground state solutions. Some of the available frameworks are more adequate to derive certain qualitative proper- ties; we illustrate this in the second half of this survey, where we also review some of the most recent literature dealing mainly with symmetry, concentra- tion, and multiplicity results. This paper contains some original results as well as new proofs and approaches to known facts.

POSITIVE SOLUTIONS FOR A FOURTH-ORDER QUASILINEAR EQUATION WITH CRITICAL SOBOLEV EXPONENT

We consider a fourth-order quasilinear equation depending on a positive parameter ∊ and with critical growth. Such equation is equivalent to a critical Hamiltonian system and the main goal of this work is to prove the existence of at least two positive solutions when the parameter ∊ is sufficiently small.

A fourth-order equation with critical growth: the effect of the domain topology

In this paper we prove the existence of multiple classical solutions for the fourth-order problem where

Local minimizers in spaces of symmetric functions and applications

\Omega

On the finite space blow up of the solutions of the Swift–Hohenberg equation

is a smooth bounded domain in

Morse index of radial nodal solutions of Hénon type equations in dimension two

\rn

Critical and noncritical regions on the critical hyperbola

,

Critical Hyperbolas and Multiple Symmetric Solutions to Some Strongly Coupled Elliptic Systems

N\geq8

Sobolev spaces of symmetric functions and applications

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