Positive solutions for the one-dimensional Sturm-Liouville superlinear p-Laplacian problem
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Date
2018-04-17
Authors
Chu, Khanh Duc
Hai, Dang Dinh
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We prove the existence of positive classical solutions for the p-Laplacian problem
-(r(t)φ(u′))′ = ƒ(t, u), t ∈ (0, 1),
au(0) - bφ-1 (r(0))u′(0) = 0, cu(1) + dφ-1 (r(1))u′(1) = 0,
where φ(s) = |s|p-2s, p > 1, ƒ : (0, 1) x [0, ∞) → ℝ is a Carathéodory function satisfying
lim supz → 0+ ƒ(t, z)/zp-1 < λ1 < lim infz → ∞ ƒ(t, z)/zp-1
uniformly for a.e. t ∈ (0, 1), where λ1 denotes the principal eigenvalue of -(r(t)φ(u′))′ with Sturm-Liouville boundary conditions. Our result extends a previous work by Manásevich, Njoku, and Zanolin to the Sturm-Liouville boundary conditions with more general operator.
Description
Keywords
p-Laplacian, Superlinear, Positive solutions
Citation
Chu, K. D., & Hai, D. D. (2018). Positive solutions for the one-dimensional Sturm-Liouville superlinear p-Laplacian problem. <i>Electronic Journal of Differential Equations, 2018</i>(92), pp. 1-14.
Rights
Attribution 4.0 International