Singularly perturbed elliptic problems with nonautonomous asymptotically\n linear nonlinearities

2014/05/28 by Liliane A. Maia, Eugenio Montefusco, Maia, Liliane +3
Mathematics · Computer Science · #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1405.7166

Abstract

We consider a class of singularly perturbed elliptic problems with\nnonautonomous asymptotically linear nonlinearities. The dependence on the\nspatial coordinates comes from the presence of a potential and of a function\nrepresenting a saturation effect. We investigate the existence of nontrivial\nnonnegative solutions concentrating around local minima of both the potential\nand of the saturation function. Necessary conditions to locate the possible\nconcentration points are also given.\n

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