In the present paper, we consider a non-local fractional equation. A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least one non-trivial and non-negative (non-positive) solution, provided the parameters lambda and mu lie in a suitable range. The existence result obtained in the present paper may be seen as a bifurcation theorem, which extends some results, well known in the classical Laplace setting, to the non-local fractional framework.
A bifurcation result for nonlocal fractional equations
Molica Bisci Giovanni;Servadei Raffaella
2015
Abstract
In the present paper, we consider a non-local fractional equation. A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least one non-trivial and non-negative (non-positive) solution, provided the parameters lambda and mu lie in a suitable range. The existence result obtained in the present paper may be seen as a bifurcation theorem, which extends some results, well known in the classical Laplace setting, to the non-local fractional framework.File in questo prodotto:
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