Positive solutions for second-order boundary-value problems with phi-Laplacian
Date
2016-02-18
Authors
Herlea, Diana-Raluca
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the existence, localization and multiplicity of positive solutions for the boundary-value problem
(ϕ(u′))′ + ƒ(t, u) = 0,
u(0) - αu′(0) = u′(1) = 0,
where ƒ : [0, 1] x ℝ+ → ℝ+ is a continuous function and ϕ : ℝ → (-b, b) is an increasing homeomorphism with ϕ(0) = 0. We obtain existence, localization and multiplicity results of positive solutions using Krasnosel'skiĭ fixed point theorem in cones, and a weak Harnack type inequality. Concerning systems, the localization is established by the vector version of Krasnosel'skiĭ theorem, where the compression-expansion conditions are expressed on components.
Description
Keywords
Positive solution, phi-Laplacian, Boundary value problem, Krasnosel'skii fixed point theorem, Weak Harnack inequality
Citation
Herlea, D. R. (2016). Positive solutions for second-order boundary-value problems with phi-Laplacian. Electronic Journal of Differential Equations, 2016(51), pp. 1-8.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.