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Existence of three solutions for a class of anisotropic variable exponent problems. (English) Zbl 1363.58006

Summary: The aim of this paper is to establish a multiplicity result for an eigenvalue anisotropic variable exponent problem which involves a nonlinearity fulfilling a non-standard growth condition. Precisely, a recent critical point result for differentiable functionals is exploited in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three weak solutions in an appropriate variable exponent Sobolev space.

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35J60 Nonlinear elliptic equations
35J70 Degenerate elliptic equations
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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