N. Alaa (1996)
Extracta Mathematicae
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The purpose of this note is to study existence of weak solutions for the quasilinear elliptic problem with Dirichlet boundary conditions.
H. Brézis, L. Nirenberg (1978)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Philippe Clément, Guido Sweers (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Isabeau Birindelli, Françoise Demengel (2004)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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J. A. Aguilar Crespo, I. Peral Alonso (1996)
Rendiconti del Seminario Matematico della Università di Padova
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Robert Dalmasso (1995)
Revista Matemática Iberoamericana
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In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system -u'' = g(v), -v'' = f(u) in (-R,R), u(±R) = v(±R) = 0 where f and g satisfy some appropriate conditions. Our result applies, in particular, to g(v) = v, f(u) = u, p > 1, or f(u) = λu + au + ... + au, with p > 1, a > 0 for j = 1, ..., k and 0 ≤ λ < μ where μ = π/4R.
Jean Vélin, François De Thélin (1993)
Revista Matemática de la Universidad Complutense de Madrid
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In this paper we give some existence and nonexistence results of non trivial solutions of nonlinear elliptic systems involving the p-Laplacian.