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POSITIVE SOLUTIONS TO p(x)-LAPLACIAN–DIRICHLET PROBLEMS WITH SIGN-CHANGING NON-LINEARITIES
Published online by Cambridge University Press: 25 August 2010
Abstract
Consider the p(x)-Laplacian–Dirichlet problem with sign-changing non-linearity of the form
where 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.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2010
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