POSITIVE SOLUTIONS TO p(x)-LAPLACIAN–DIRICHLET PROBLEMS WITH SIGN-CHANGING NON-LINEARITIES
2010 ◽
Vol 52
(3)
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pp. 505-516
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Keyword(s):
AbstractConsider 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.
1998 ◽
Vol 39
(3)
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pp. 386-407
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2004 ◽
Vol 134
(1)
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pp. 137-141
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2006 ◽
Vol 11
(4)
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pp. 323-329
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1999 ◽
Vol 42
(2)
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pp. 349-374
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1977 ◽
Vol 29
(5)
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pp. 1081-1085
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Keyword(s):