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Existence of a non-trivial solution for the -Laplacian equation with Fučík type resonance at infinity. II

✍ Scribed by Mieko Tanaka

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 761 KB
Volume: 71
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2009.01.186

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✦ Synopsis

We prove the existence of a non-trivial weak solution for the equation

by variational methods. We consider the case where a = λ 1 or b = λ 1 (λ 1 denotes the first eigenvalue of -∆ p ), or the case where a is close to b, while the nonlinearity f belongs to a class that contains, for example, |u| q-2 u (1 < q < p).

📜 SIMILAR VOLUMES

Existence of a non-trivial solution for

Existence of a non-trivial solution for the p-Laplacian equation with Fučík type resonance at infinity

✍ Mieko Tanaka 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 586 KB

We prove the existence of a non-trivial weak solution for the equation by variational methods. We consider the case where a = λ 1 or b = λ 1 , while the nonlinearity f belongs to a class that contains, for example, |u| q-2 u (1 < q < p).