An approach to nonlinear elliptic boundary value problems

Tarafdar E. (1983) An approach to nonlinear elliptic boundary value problems. Journal of the Australian Mathematical Society, 34 3: 316-335. doi:10.1017/S1446788700023752


Author Tarafdar E.
Title An approach to nonlinear elliptic boundary value problems
Journal name Journal of the Australian Mathematical Society   Check publisher's open access policy
ISSN 1446-8107
Publication date 1983-01-01
Sub-type Article (original research)
DOI 10.1017/S1446788700023752
Volume 34
Issue 3
Start page 316
End page 335
Total pages 20
Subject 2600 Mathematics
Abstract Let D ⊂ Rn be a bounded domain and L: dom L ⊂ L2{D) → L2(D) be a self-adjoint operator of finite dimensional kernel. Let f: D × R → R be a function satisfying the Carathéodory condition. Assume that there are constants λ > 0 and δ ∊ [0,1) such that Then with the aid of a generalized Krasnosel'skii's theorem it has been proved that under conditions exactly analogous to those of Landesman and Lazer there exists u ∊ L2(D) such that L(u)(x) = f(x, u(x)) for ∀x ∊ D. This result is then used to prove the existence of weak solutions of nonlinear elliptic boundary value problems. Other abstract results applicable to ordinary and partial differential equations have also been proved.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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Created: Sat, 09 Jul 2016, 17:07:11 EST by System User