APPLICATION OF MOUNTAIN PASS THEOREM TO SUPERLINEAR EQUATIONS WITH FRACTIONAL LAPLACIAN CONTROLLED BY DISTRIBUTED PARAMETERS AND BOUNDARY DATA

作者：Bors Dorota^*

来源：Discrete and Continuous Dynamical Systems-Series B, 2018, 23(1): 29-43.

DOI：10.3934/dcdsb.2018003

• Boundary value problems
• fractional Laplacian
• stability
• Mountain Pass Theorem

In the paper we consider a boundary value problem involving a differential equation with the fractional Laplacian (-Delta)(alpha/2) for alpha is an element of(1, 2) and some superlinear and subcritical nonlinearity G(z) provided with a nonhomogeneous Dirichlet exterior boundary condition. Some sufficient conditions under which the set of weak solutions to the boundary value problem is nonempty and depends continuously in the Painleve-Kuratowski sense on distributed parameters and exterior boundary data are stated. The proofs of the existence results rely on the Mountain Pass Theorem.

• 出版日期2018-1