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Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional -Laplacian

✍ Scribed by Yūki Naito; Satoshi Tanaka

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
348 KB
Volume
69
Category
Article
ISSN
0362-546X

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✦ Synopsis

We consider the boundary value problem involving the one-dimensional p-Laplacian

where p > 1. We establish sharp conditions for the existence of solutions with prescribed numbers of zeros in terms of the ratio f (s)/s p-1 at infinity and zero. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.

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Existence of positive solutions for the
Existence of positive solutions for the one-dimensional singular -Laplacian
✍ Zheng-an Yao; Wenshu Zhou 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 235 KB

This paper concerns the positive solutions of boundary value problems for the one-dimensional singular p-Laplacian. By the classical method of elliptic regularization, we obtain some existence results which generalize some results of [W. Zhou, X. Wei, Positive solutions to BVPs for a singular differ