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On the existence of bounded solutions of nonlinear elliptic systems

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  • Abdelaziz Ahammou

Abstract

We study the existence of bounded solutions to the elliptic system − Δ p u = f ( u , v ) + h 1 in Ω , − Δ q v = g ( u , v ) + h 2 in Ω , u = v = 0 on ∂ Ω , non-necessarily potential systems. The method used is a shooting technique. We are concerned with the existence of a negative subsolution and a nonnegative supersolution in the sense of Hernandez; then we construct some compact operator T and some invariant set K where we can use the Leray Schauder's theorem.

Suggested Citation

  • Abdelaziz Ahammou, 2002. "On the existence of bounded solutions of nonlinear elliptic systems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 30, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:735239
    DOI: 10.1155/S0161171202010293
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