A Perturbation Method in Critical Point Theory and Applications
Open Access
- 1 September 1981
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 267 (1) , 1-32
- https://doi.org/10.2307/1998565
Abstract
This paper is concerned with existence and multiplicity results for nonlinear elliptic equations of the type <!-- MATH $- \Delta u = {\left| u \right|^{p - 1}}u + h(x)$ --> in <!-- MATH $\Omega ,\,u = 0$ --> on <!-- MATH $\partial \Omega$ --> . Here, <!-- MATH $\Omega \subset {{\mathbf{R}}^N}$ --> is smooth and bounded, and <!-- MATH $h \in {L^2}(\Omega )$ --> is given. We show that there exists 1$"> such that for any <!-- MATH $p \in (1,\,{p_N})$ --> and any <!-- MATH $h \in {L^2}(\Omega )$ --> , the preceding equation possesses infinitely many distinct solutions.
Keywords
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