Existence and a Priori Estimates for Positive Solutions of p-Laplace Systems
- Azizieh, Céline
- Clément, Philippe
- Mitidieri, Enzo
DOIAbstract
AbstractWe use continuation and moving hyperplane methods to prove some existence and a priori estimates for p-Laplace systems of the form−Δp1u=f(∣v∣) in Ω,u=0 on ∂Ω,−Δp2v=g(∣u∣) in Ω,v=0 on ∂Ω, where 1<p1,p2<N, Ω⊂RN is bounded and convex, and f,g : R→R+ are nondecreasing locally Lipschitz continuous functions satisfyingC1∣s∣q1⩽f(s)⩽C2∣s∣q1,D1∣s∣q2⩽g(s)⩽D2∣s∣q2 ∀s∈R+ for some positive constants C1,C2,D1,D2 and q1q2(p1−1)(p2−1). We extend results obtained in Azizieh and Clément (J. Differential Equations, 179 (2002), 213–245) where the case of a single equation was considered
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