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.
Mountain pass solutions for non-local elliptic operators.Journal of Mathematical Analysis and Applications, 389(2):887–898
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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.