Geodesic
POSITIVE SOLUTIONS TO p(x)-LAPLACIAN–DIRICHLET PROBLEMS WITH SIGN-CHANGING NON-LINEARITIES
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 505-516

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DOI

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.
DOI : 10.1017/S0017089510000388
Mots-clés : 35J70 
FAN, XIANLING. POSITIVE SOLUTIONS TO p(x)-LAPLACIAN–DIRICHLET PROBLEMS WITH SIGN-CHANGING NON-LINEARITIES. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 505-516. doi: 10.1017/S0017089510000388
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     author = {FAN, XIANLING},
     title = {POSITIVE {SOLUTIONS} {TO} {p(x)-LAPLACIAN{\textendash}DIRICHLET} {PROBLEMS} {WITH} {SIGN-CHANGING} {NON-LINEARITIES}},
     journal = {Glasgow mathematical journal},
     pages = {505--516},
     year = {2010},
     volume = {52},
     number = {3},
     doi = {10.1017/S0017089510000388},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000388/}
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