In:
Advanced Nonlinear Studies, Walter de Gruyter GmbH, Vol. 16, No. 3 ( 2016-08-01), p. 529-550
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.
Type of Medium:
Online Resource
ISSN:
1536-1365
,
2169-0375
DOI:
10.1515/ans-2015-5033
Language:
English
Publisher:
Walter de Gruyter GmbH
Publication Date:
2016
detail.hit.zdb_id:
2482156-1
SSG:
17,1
Permalink