For a nonlinear biharmonic equation on a locally finite graph, ground state solutions exist for any lambda>1, p>2, and as lambda tends to infinity they converge to a ground state solution of the limit problem on the potential well.
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Existence and convergence of solutions for nonlinear biharmonic equations on graphs
For a nonlinear biharmonic equation on a locally finite graph, ground state solutions exist for any lambda>1, p>2, and as lambda tends to infinity they converge to a ground state solution of the limit problem on the potential well.