A limiting problem for a family of eigenvalue problems involving p-Laplacians
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In this paper we analyse the existence of principal eigenvalues and eigenfunctions for a family of eigenvalue problems described by a system consisting in two partial differential equations involving p-Laplacians. Next, we study the asymptotic behaviour, as \(p\rightarrow \infty \), of the sequence of principal eigenfunctions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions.
KeywordsEigenvalue problem Weak solution Distance function \(\Gamma \)-convergence Viscosity solution
Mathematics Subject Classification35D30 35D40 46E30 46E35 49J40 49J45
The research of MM and DSD was partially supported by CNCS-UEFISCDI Grant No. PN-III-P4-ID-PCE-2016-0035 while JDR was partially supported by CONICET Grant PIP GI No 11220150100036CO (Argentina), by UBACyT Grant 20020160100155BA (Argentina) and by MINECO MTM2015-70227-P (Spain).
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