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The existence of multiple solutions to quasilinear elliptic equations. (English) Zbl 1122.35033
Summary: Using Morse theory and the truncation technique, a proof is given of the existence of at least three nontrivial solutions for a class of \(p\)-Laplacian equations. When \(p=2\), the existence of four nontrivial solutions is also considered.

MSC:
35J60 Nonlinear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
47J30 Variational methods involving nonlinear operators
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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