MULTIPLE SOLUTIONS FOR PERTURBED NON-LOCAL FRACTIONAL LAPLACIAN EQUATIONS

作者：Ferrara Massimiliano^*; Guerrini Luca; Zhang Binlin

来源：Electronic Journal of Differential Equations, 2013, 260.

• Variational methods
• integrodifferential operators
• fractional Laplacian

In article we consider problems modeled by the non-local fractional Laplacian equation
(-Delta)(s)u = lambda f(x, u) + mu g(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, mu are real parameters, Omega is an open bounded subset of R-n (n > 2s) with Lipschitz boundary partial derivative Omega and f, g: Omega R -> R are two suitable Caratheodory functions. By using variational methods in an appropriate abstract framework developed by Servadei and Valdinoci [17] we prove the existence of at least three weak solutions for certain values of the parametes.

• 出版日期2013-11-26
• 单位黑龙江工程学院