Publication: Nodal Solutions to Quasilinear Elliptic Problems Involving the 1-Laplacian Operator via Variational and Approximation Methods
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Undergraduate course
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Indiana Univ Math Journal
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Abstract
In this work we use two different methods to get nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator. In the first one, we develop an approach based on a minimization of the energy functional associated with a problem involving the 1-Laplacian operator in R-N, on a subset of the Nehari set which contains just sign-changing functions. In the second part we obtain a nodal solution to a quasilinear elliptic problem involving the 1-Laplacian operator in a bounded domain, through a thorough analysis of the sequence of solutions of the p-Laplacian problem associated with it, as p -> 1(+). In both cases, several technical difficulties appear in comparison with the related results involving signed solutions.
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Keywords
1-Laplacian operator, Nehari method, nodal solutions
Language
English
Citation
Indiana University Mathematics Journal. Bloomington: Indiana Univ Math Journal, v. 71, n. 2, p. 439-462, 2022.
