Upper and Lower Solution Method and a Singular Boundary Value Problem for the One-Dimensional p-Laplacian

By Daqing Jiang, Wenjie Gao. 2000

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Abstract The singular boundary value problem Φ u ′ ′ = −g t , u , for all t ∈ 0, 1 , u 0 = u 1 = 0, is studied in this paper with Φ(s) = |s|p − 2s, p > 1. The singularity may appear at u = 0, t = 0, and t = 1, and the function g may change sign. The existence of solutions is obtained via an upper and lower solution method.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7830ff0bdab5fe622e4abafc67c0056d62f660c7