A Semilinear Dirichlet Problem
- 1 April 1979
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 31 (2) , 337-340
- https://doi.org/10.4153/cjm-1979-037-9
Abstract
Introduction and notations. Let Ω be a bounded region in Rn. 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 × Rn+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.Keywords
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