Ding, Ling; Li, Lin; Bisci, Giovanni Molica Existence of three solutions for a class of anisotropic variable exponent problems. (English) Zbl 1363.58006 Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 77, No. 3, 41-52 (2015). 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. Cited in 2 Documents 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.) Keywords:critical point; weak solutions; anisotropic variable exponent problems PDFBibTeX XMLCite \textit{L. Ding} et al., Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 77, No. 3, 41--52 (2015; Zbl 1363.58006)