Existence of positive solutions for two nonlinear eigenvalue problems

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belhaj.pdf (228.74 KB)
Date
2003-02-15
Authors
Rhouma, Nedra BelHaj
Maatoug, Lamia
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We study the existence of positive solutions for the following two nonlinear eigenvalue problems ∆u - g(., u)u + λƒ(.,u) = 0, ∆u - g(., u)u + λƒ(., u) = 0, in a bounded regular domain in ℝ2 with u = 0 on the boundary. We assume that ƒ and g are in Kato class of functions.
Description
Keywords
Eigenvalue, Kato class, Green's function, Superharmonic function, Shauder fixed point theorem, Maximum principle
Citation
Rhouma, N. B., & Maatoug, L. (2003). Existence of positive solutions for two nonlinear eigenvalue problems. <i>Electronic Journal of Differential Equations, 2003</i>(16), pp. 1-16.
URI
https://hdl.handle.net/10877/12607
Collections
Electronic Journal of Differential Equations