J.V. Goncalves

Critical Point Theory for Nondifferentiable Functionals and Applications

Abstract We consider minimization results for locally Lipschitzian functionals on a Banach space by introducing a compactness condition of the Palais-Smale type which is suggested by the Variational Principle of Ekeland. Applications are given to some semilinear elliptic problems with discontinuous nonlinearities.

Existence and multiplicity results for a class of nonlinear elliptic boundary value problems at resonance

are positive and form an increasing sequence ,I, 0 in Sz which, by the maximum principle, satisfies @,/an < 0 on 30, where

ON A CLASS OF QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL EXPONENTS

This paper deals with the following class of quasilinear elliptic problems in radial form where α, β, δ, l, γ, q are given real numbers, λ > 0 is a parameter and 0 < R < ∞. Some results on the existence of positive solutions are obtained by combining the Mountain Pass Theorem with an argument used by Brezis and Nirenberg to overcome the lack of compactness due to the presence of critical Sobolev exponents.

On the Uniqueness of Solution for a Class of Semilinear Elliptic Problems

We shall discuss here the uniqueness of solution of the Dirichlet problem \( - \Updelta u = f(u) + \rho h(x)\quad {\text{in}}\,\Upomega , {\text{ u = 0}}\quad {\text{on }}\partial \Upomega , \) for large values of the real parameter \( \rho \).

ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS

We employ arguments involving continua of fixed points of suitable nonlinear compact operators and the Lyapunov–Schmidt method to prove existence and multiplicity of solutions in a class of fourth order non-homogeneous resonant elliptic problems. Our main result extends even similar ones known for the Laplacian.