Geodesic
POSITIVE SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN PROBLEMS
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 571-578

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DOI

We consider the systemwhere p(x), q(x) ∈ C1(RN) are radial symmetric functions such that sup|∇ p(x)| < ∞, sup|∇ q(x)| < ∞ and 1 < inf p(x) ≤ sup p(x) < ∞, 1 < inf q(x) ≤ sup q(x) < ∞, where −Δp(x)u = −div(|∇u|p(x)−2∇u), −Δq(x)v = −div(|∇v|q(x)−2∇v), respectively are called p(x)-Laplacian and q(x)-Laplacian, λ1, λ2, μ1 and μ2 are positive parameters and Ω = B(0, R) ⊂ RN is a bounded radial symmetric domain, where R is sufficiently large. We prove the existence of a positive solution whenfor every M > 0, and . In particular, we do not assume any sign conditions on f(0), g(0), h(0) or γ(0).
DOI : 10.1017/S0017089509005199
Mots-clés : 35J60, 35B30, 35B40 
AFROUZI, G. A.; GHORBANI, H. POSITIVE SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN PROBLEMS. Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 571-578. doi: 10.1017/S0017089509005199
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     title = {POSITIVE {SOLUTIONS} {FOR} {A} {CLASS} {OF} {p(x)-LAPLACIAN} {PROBLEMS}},
     journal = {Glasgow mathematical journal},
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     year = {2009},
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     number = {3},
     doi = {10.1017/S0017089509005199},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509005199/}
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