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.
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Localization results are established for nonlocal gradient-based optimal control problems by taking the fractional parameter to 1 or the horizon parameter to 0 in two specific energy settings.
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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.
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Localization for nonlocal gradient-based optimal control problems
Localization results are established for nonlocal gradient-based optimal control problems by taking the fractional parameter to 1 or the horizon parameter to 0 in two specific energy settings.