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Nonlinear eigenvalue problems for quasilinear equations in unbounded domains
Author(s) -
Drábek Pavel,
Simader Christian G.
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.1999.3212030102
Subject(s) - mathematics , nonlinear system , eigenvalues and eigenvectors , mathematical analysis , pure mathematics , physics , quantum mechanics
Abstract We prove the existence of a solution of the nonlinear equation\documentclass{article}\pagestyle{empty}\begin{document}$$ ‐ {\rm div}\left({a\left(x \right)|\nabla _u |^{p ‐ 2} \nabla _u} \right) = \lambda f\left({x,u} \right) $$\end{document}in IR N and in exterior domains, respectively. We concentrate to the case when p ≥ N and the nonlinearity f(x, · ) is “superlinear” and “subcritical”.