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A Semilinear Dirichlet Problem

Published online by Cambridge University Press:  20 November 2018

Alfonso Castro
Alfonso Castro*
Affiliation:
Centro de Investigacion del IPN, Mexico
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 337 - 340
Copyright
Copyright © Canadian Mathematical Society 1979

References

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