A Brezis-Nirenberg splitting approach for nonlocal fractional equations

作者：Bisci Giovanni Molica^*; Servadei Raffaella

来源：Nonlinear Analysis-Theory Methods & Applications, 2015, 119: 341-353.

DOI：10.1016/j.na.2014.10.025

• Fractional Laplacian
• Nonlocal problems
• Variational methods
• Critical point theory
• Integrodifferential operators

In this paper we consider problems modeled by the following nonlocal fractional equation
{(-Delta)(s)u + a(x)u = mu f(u) in Omega
u = 0 in R-n \ Omega,
where s is an element of(0, 1) is fixed, Omega is an open bounded subset of R-n, n > 2s, with Lipschitz boundary, (-Delta)(s) is the fractional Laplace operator and mu is a real parameter.
Under two different types of conditions on the functions a and f, by using a famous critical point theorem in the presence of splitting established by Brezis and Nirenberg, we obtain the existence of at least two nontrivial weak solutions for our problem.

• 出版日期2015-6