4.6 Article

Existence of infinitely many solutions for an anisotropic equation using genus theory

Journal

MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 45, Issue 12, Pages 7591-7606

Publisher

WILEY
DOI: 10.1002/mma.8264

Keywords

anisotropic operator; critical growth; genus theory; Laplacian; subcritical growth

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Using genus theory, this paper proves the existence of infinitely many solutions for an anisotropic equation involving subcritical growth, as well as the existence of k-pairs of distinct solutions using Krasnoselskii genus and Clark's theorem. Furthermore, the existence of infinitely many solutions for an anisotropic equation involving critical growth is studied.
Using genus theory, the existence of infinitely many solutions for an anisotropic equation involving the subcritical growth is proved. Also, by using Krasnoselskii genus and Clark's theorem, the existence of k-pairs of distinct solutions is proved. Finally, the existence of infinitely many solutions for an anisotropic equation involving the critical growth is studied.

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