Existence of solutions for nonlocal equations with super-quadratic nonlinearities is shown via the Mountain Pass Theorem under mild kernel assumptions, with numerical simulations via energy-based gradient descent.
Analysis of a scalar nonlocal peridynamic model with a sign changing kernel.Discrete & Con- tinuous Dynamical Systems-B, 18(5):1415, 2013
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A Mountain-Pass Algorithm for Nonlocal Problems with Super-quadratic Nonlinearities
Existence of solutions for nonlocal equations with super-quadratic nonlinearities is shown via the Mountain Pass Theorem under mild kernel assumptions, with numerical simulations via energy-based gradient descent.