Existence of weak solutions for non-local fractional problems via Morse theory

Massimiliano Ferrara; Giovanni Molica Bisci; Binlin Zhang

doi:10.3934/dcdsb.2014.19.2483

Article Contents

2014, Volume 19, Issue 8: 2483-2499. Doi: 10.3934/dcdsb.2014.19.2483

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Existence of weak solutions for non-local fractional problems via Morse theory

1.
University of Reggio Calabria and CRIOS University Bocconi of Milan, Via dei Bianchi presso Palazzo Zani, 89127 Reggio Calabria
2.
Dipartimento P.A.U., Università degli Studi Mediterranea di Reggio Calabria, Salita Melissari - Feo di Vito, 89100 Reggio Calabria
3.
Department of Mathematics, Heilongjiang Institute of Technology, 150050 Harbin

Received: October 31, 2013

Revised: January 31, 2014

Published: September 2014

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Abstract

In this paper, we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. Non-trivial solutions are obtained by computing the critical groups and Morse theory. Our results extend some classical theorems for semilinear elliptic equations to the non-local fractional setting.

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Mathematics Subject Classification: 35J60, 35J91, 58E05.

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