Djairo Guedes de Figueiredo

A maximum principle for an elliptic system and applications to semilinear problems

The Dirichlet problem in a bounded region for elliptic systems of the form (*) ( - Updelta u = fleft( {x,u} right) - v,quad - Updelta v = delta u - gamma v ) is studied. For the question of existence of positive solutions the key ingredient is a maximum principle for a linear elliptic system associated with (*). A priori bounds for the solutions of (*) are proved under various types of growth conditions on f. Variational methods are used to establish the existence of pairs of solutions for (*).

A Variational Approach to Superlinear Elliptic Problems

This paper contains a variational treatment of the Ambrosetti-Prodi problem, including the superlinear case. The main result extends previous ones by Kazdan-Warner, Amann-Hess, Dancer, K. C. Chang and de Figueiredo. The required abstract results on critical point theory of functionals in Hilbert space are all proved using Ekeland’s variational principle. These results apply as well to other superlinear elliptic problems provided an ordered pair of a sub- and a supersolution is exhibited.

Perturbations of Second Order Linear Elliptic Problems by Nonlinearities Without Landesman–Lazer Condition

L et ℒ be a second order symmetric uniformly elliptic operator with smooth coefficients acting on real valued functions defined in a bounded smooth domain Ω in RN.

On The Superlinear Ambrosetti–Prodi Problem

L et be a smooth bounded domain in R N . We consider the semilinear elliptic boundary value problem.

Nonlinear Perturbations of a Linear Elliptic Problem Near Its First Eigenvalue

In this paper we investigate the existence of solutions for the Dirichlet problem Lu = f(x, u), in ( varOmega . )

The Dirichlet Problem for Nonlinear Elliptic Equations: A Hilbert Space Approach

Let ( Upomega ) be a bounded domain in RN, and ( {text{Lu}} = sumnolimits_{left| upalpha right| le text{m};left| upbeta right| le text{m}} {( - 1)^{left| upbeta right|} text{D}^{upbeta } } (text{a}_{upalpha upbeta } (text{x})text{D}^{upalpha }text{u}) ) be a uniformly strongly elliptic operator acting on functions defined in ( Upomega ).

On Pairs of Positive Solutions for a Class of Semilinear Elliptic Problems.

The question of existence of positive solutions for semilinear elliptic problems of the type −Δu = f(u) in Ω, u = 0 on ∂Ω, depends very strongly on the behavior of the function f: R + → R at 0 and at +∞.

SEMILINEAR ELLIPTIC EQUATIONS AT RESONANCE: HIGHER EIGENVALUES AND UNBOUNDED NONLINEARITIES

1. Let L be a uniformly strongly elliptic operator of order 2 m with smooth coefficients acting on real–valued functions defined in a bounded domain Ω in RN.

Positive Solutions for Some Classes of Semilinear Elliptic Problems

Let us consider the Dirichlet problem ( - Updelta u = fleft( u right) ) and ( u > 0 ) in ( Upomega ) , u = 0 on ( partial Upomega ).

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 ).