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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

XIANLING FAN
XIANLING FAN*
Affiliation:
Department of Mathematics, Lanzhou City University, Lanzhou 730070, PR China Department of Mathematics, Lanzhou University, Lanzhou 730000, PR China e-mail: fanxl@lzu.edu.cn
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Abstract

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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.

Keywords

35J70
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 505 - 516
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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