Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 257, pp. 18.
Ground state solution of a nonlocal boundaryvalue problem
Cyril Joel Batkam
Abstract:
In this article, we apply the Nehari manifold method to study
the Kirchhoff type equation
subject to Dirichlet boundary conditions. Under a general 4superlinear
condition on the nonlinearity f, we prove the existence of a ground
state solution, that is a nontrivial solution which has least energy
among the set of nontrivial solutions. If f is odd with respect
to the second variable, we also obtain the existence of infinitely
many solutions. Under our assumptions the Nehari manifold does not
need to be of class C^1.
Submitted June 24, 2013. Published November 22, 2013.
Math Subject Classifications: 35J60, 35J25.
Key Words: Nonlocal problem; Kirchhoff's equation; ground state solution;
Nehari manifold.
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Cyril Joel Batkam
Département de mathématiques
Université de Sherbrooke
Sherbrooke, Québec, J1K 2R1, Canada
email: cyril.joel.batkam@usherbrooke.ca

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