Geodesic
A Semilinear Dirichlet Problem
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 337-340

Voir la notice de l'article provenant de la source Cambridge University Press

Introduction and notations. Let Ω be a bounded region in R n . In this note we discuss the existence of weak solutions (see [4, Section 2]) of the Dirichlet problem (I) where Δ is the Laplacian operator, g : Ω × R → R and f : Ω × R n+1 → R are functions satisfying the Caratheodory condition (see [2, Section 3]), and ∇ is the gradient operator.We let λ1 < λ2 ≦ ... ≦ λm ≦ ... denote the sequence of numbers for which the problem (II) has nontrivial weak solutions. 
Castro, Alfonso. A Semilinear Dirichlet Problem. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 337-340. doi: 10.4153/CJM-1979-037-9
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