Multiple solutions to elliptic inclusions via critical point theory on closed convex sets

Salvatore A. Marano; Sunra J. N. Mosconi

doi:10.3934/dcds.2015.35.3087

Article Contents

2015, Volume 35, Issue 7: 3087-3102. Doi: 10.3934/dcds.2015.35.3087

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Multiple solutions to elliptic inclusions via critical point theory on closed convex sets

Salvatore A. Marano^1, and
Sunra J. N. Mosconi^1,

1.
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania

Received: July 31, 2014

Revised: September 30, 2014

Published: May 2017

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Abstract

The existence of multiple solutions $u\in H^1_0(\Omega)$ to a differential inclusion of the type $-\Delta u\in \partial J(x,u)$ in $\Omega$, where $\partial J(x,\cdot)$ denotes the generalized sub-differential of $J(x,\cdot)$, is investigated through critical point theorems for locally Lipschitz continuous functionals on closed convex sets of a Hilbert space.

Keywords:

Critical point,
function defined on a closed convex set,
Schauder condition,
elliptic differential inclusion,
multiple solutions.

Mathematics Subject Classification: Primary: 58E05, 49J35; Secondary: 49J57.

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