Chu, Khanh DucHai, Dang Dinh2022-01-312022-01-312018-04-17Chu, 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. 1-14.1072-6691https://hdl.handle.net/10877/15259We 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.Text14 pages1 file (.pdf)enAttribution 4.0 Internationalp-LaplacianSuperlinearPositive solutionsArticle