Cyril Joel Batkam
In this article, we apply the Nehari manifold method to study the Kirchhoff type equation
subject to Dirichlet boundary conditions. Under a general 4-superlinear 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
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