A Semilinear Dirichlet Problem

Authors

Alfonso Castro, Harvey Mudd CollegeFollow

Document Type

Article - preprint

Department

Mathematics (HMC)

Publication Date

1979

Abstract

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:

Δu(x) + g(x, u(x)) + f(x, u(x), ∇u(x)) = 0 ; x є Ω

u(x) = 0 ; x є ∂Ω

where Δ is the Laplacian operator, g : Ω x R → R and f : Ω x Rⁿ⁺¹ → R are functions satisfying the Caratheodory condition (see [2, Section 3]), and ∇ is the gradient operator.

Comments

Author's pre-print manuscript available for download.

For the publisher's PDF, please visit http://dx.doi.org/10.4153/CJM-1979-037-9

Rights Information

© 1979 Canadian Mathematical Society

DOI

10.4153/CJM-1979-037-9

Recommended Citation

Castro, Alfonso. “A semilinear Dirichlet problem” Canadian J. of Math., Vol. XXXI, No. 2(1979), pp. 337-340.