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 nonpositive mixed local–nonlocal operators.Frac- tional Calculus and Applied Analysis, 26(3):943–961
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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.