Positive solutions for second-order boundary-value problems with phi-Laplacian

Date

2016-02-18

Authors

Herlea, Diana-Raluca

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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. <i>Electronic Journal of Differential Equations, 2016</i>(51), pp. 1-8.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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