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arXiv · 1311.2204

Ground state solution of a nonlocal boundary-value problem

Cyril Joel Batkam
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Abstract

In this paper, we apply the method of the Nehari manifold to study the Kirchhoff type equation \begin{equation*} -\Big(a+b\int_Ω|\nabla u|^2dx\Big)Δu=f(x,u) \end{equation*} submitted 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. In case which $f$ 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 $\mathcal{C}^1$.

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Cyril Joel Batkam. 2013-12-19. Ground state solution of a nonlocal boundary-value problem. https://arxiv.org/abs/1311.2204

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