Existence of positive solutions for a class of the p-Laplace equations
- 1 October 1994
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 36 (2) , 249-264
- https://doi.org/10.1017/s0334270000010390
Abstract
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.Keywords
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