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ABSTRACT: In this work we give necessary and sufficient conditions for having a maximum principle for cooperative elliptic systems involving p-Laplacian operator on the whole $mathbb{R}^{N}$. This principle is then used to yield solvability for the cooperative elliptic systems by an approximation method.
Electronic Journal of Differential Equations. 01/2010;
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ABSTRACT: We show the existence of a first curve in the FuÄÂik spectrum with weights for the p-Laplacian under mixed boundary conditions. We also study the asymptotic behavior of this first curve.
International Journal of Mathematics and Mathematical Sciences. 01/2007;
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ABSTRACT: We work on the whole $R^N$ and prove the existence of a first nonprincipal eigenvalue for an asymmetric problem with weights involving the p-Laplacian. As an application we obtain a first nontrivial curve in the corresponding Fucik spectrum.
Electronic Journal of Differential Equations. 01/2006;