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Existence of positive solutions for a class of the p-Laplace equations

Published online by Cambridge University Press:  17 February 2009

Yin Xi Huang
Yin Xi Huang
Affiliation:
Department of Mathematical Sciences, Memphis State University, Memphis, TN 38152, U.S.A
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Abstract

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We are concerned with the existence of solutions of

where Δp is the p-Laplacian, p ∈ (1, ∞), and Ω is a bounded smooth domain in ℝn.

For h(x) ≡ 0 and f(x, u) satisfying proper asymptotic spectral conditions, existence of a unique positive solution is obtained by invoking the sub-supersolution technique and the spectral method. For h(x) ≢ 0, with assumptions on asymptotic behavior of f(x, u) as u → ±∞, an existence result is also proved.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 2 , October 1994 , pp. 249 - 264
Copyright
Copyright © Australian Mathematical Society 1994

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