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Remarks on Multiple Nontrivial Solutions for Quasi-Linear Resonant Problems

✍ Scribed by Jiaquan Liu; Jiabao Su

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 123 KB
Volume: 258
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.7374

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✦ Synopsis

In this paper Morse theory and local linking are used to study the existence of multiple nontrivial solutions for a class of Dirichlet boundary value problems with double resonance at infinity and at 0.

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Multiple nontrivial solutions for resonant Neumann problems

✍ Michael Filippakis; Nikolaos S. Papageorgiou 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 172 KB

## Abstract We consider semilinear second order elliptic Neumann problems, which are resonant both at infinity (with respect to an eigenvalue __λ__~__k__~, __k__ ≥ 1) and at zero (with respect to the principal eigenvalue __λ__~0~ = 0). Using techniques from Morse theory, combined with variational m