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Nontrivial solutions for a class of resonant -Laplacian Neumann problems

✍ Scribed by Leszek Gasiński; Nikolaos S. Papageorgiou

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
451 KB
Volume
71
Category
Article
ISSN
0362-546X

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✦ Synopsis

We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator with a Carathéodory reaction term. We assume that asymptotically at infinity resonance occurs with respect to the principal eigenvalue λ 0 = 0 (i.e., the reaction term is p -1sublinear near +∞). Using variational methods based on the critical point theory and an alternative minimax characterization of the first nonzero eigenvalue λ 1 > 0, we show that the problem has a nontrivial smooth strong solution.

📜 SIMILAR VOLUMES

Multiple nontrivial solutions for resona
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