POSITIVE SOLUTIONS TO p(x)-LAPLACIAN–DIRICHLET PROBLEMS WITH SIGN-CHANGING NON-LINEARITIES

FAN, XIANLING

Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 505-516

Résumé

Consider the p(x)-Laplacian–Dirichlet problem with sign-changing non-linearity of the formwhere Ω ⊂ RN is a bounded domain, p ∈ C0(Ω) and infx∈Ωp(x) > 1, m ∈ L∞(Ω) is non-negative, f : R → R is continuous and f(0) > 0, the coefficient a ∈ L∞(Ω) is sign-changing in (Ω). We give some sufficient conditions to assure the existence of a positive solution to the problem for sufficiently small λ > 0. Our results extend the corresponding results established in the p-Laplacian case to the p(x)-Laplacian case.

Détail

DOI : 10.1017/S0017089510000388

Mots-clés : 35J70

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