A bifurcation result for non-local fractional equations

作者：Bisci Giovanni Molica^*; Servadei Raffaella

来源：Analysis and Applications, 2015, 13(4): 371-394.

DOI：10.1142/S0219530514500067

• Variational methods
• integrodifferential operators
• fractional Laplacian

In the present paper, we consider problems modeled by the following non-local fractional equation
{ (-Delta)(s)u - lambda u = mu f (x, u) in Omega,
u = 0 in R-n\Omega,
where s is an element of (0, 1) is fixed, (-Delta)(s) is the fractional Laplace operator, lambda and mu are real parameters, Omega is an open bounded subset of R-n, n > 2s, with Lipschitz boundary and f is a function satisfying suitable regularity and growth conditions. 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.

• 出版日期2015-7