Bounded Solutions for Nonlocal Boundary Value Problems on Lipschitz Manifolds with Boundary
Abstract
We consider nonlinear nonlocal boundary value problems associated with fractional operators (including the fractional p-Laplace and the regional fractional p-Laplace operators) and subject to general (fractional-like) boundary conditions on bounded domains with Lipschitz boundary. Under suitable conditions on the nonlinearities of our system, we establish the existence of bounded solutions and provide explicit L ∞ ${L^{\infty}}$ -estimates of solutions which are optimal with respect to the inhomogeneous “sources” present in the system. As application, these results are shown to apply to a class of nonlinear nonlocal equations for the Dirichlet fractional p-Laplacian and regional fractional p-Laplace with a dissipative nonlinearity, and to a class of semilinear nonlocal boundary value problems with fractional Wentzell–Robin boundary conditions corresponding to the so-called fractional Wentzell Laplacian.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 23, 2016
- Source ID
- 10.1515/ans-2015-5033
Entities
People
- Ciprian G. Gal
- Mahamadi Warma
Organizations
- Florida International University
- University of Puerto Rico