João Marcos do Ó

On some fourth-order semilinear elliptic problems in R N

The existence of two solutions for a fourth-order semilinear elliptic problem involving critical growth from the viewpoint of Sobolev embedding was established. The basic tools used in the analysis were the mountain-pass theorem, constrained minimization, and concentration-compactness principle. The existence of positive principle eigenvalues for the corresponding linear elliptic problem was also investigated.

Periodic solutions for nonlinear equations with mean curvature-like operators

Abstract We give an existence result for a periodic boundary value problem involving mean curvature-like operators in the scalar case. Following [R. Manasevich, J. Mawhin, Periodic solutions for nonlinear systems with p -Laplacian-like operators, J. Differential Equations 145 (1998), 367–393], we use an approach based on the Leray–Schauder degree.

Multiplicity results for some quasilinear elliptic problems

In this paper, we study multiplicity of weak solutions for the following class of quasilinear elliptic problems of the form

Schrodinger-Poisson systems with a general critical nonlinearity

-\Delta_p u -\Delta u = g(u)-\lambda |u|^{q-2}u \quad \text{in } \Omega \text{ with } u=0 \text{ on } \partial\Omega,

Multiparameter Elliptic Equations in Annular Domains

where

Three positive solutions for a class of elliptic systems in annular domains

\Omega

Multiple solutions for a class of quasilinear elliptic problems

is a bounded domain in

Trudinger-Moser type inequalities for weighted Sobolev spaces involving fractional dimensions

{\mathbb R}^n