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.
Variational methods for non-local operators of elliptic type.Discrete & Continuous Dynamical Systems, 33(5):2105, 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.