Existence of Three Solutions for a Class of Nonlocal Neumann Problem
DOI:
https://doi.org/10.18311/jims/2024/32297Keywords:
Fractional Laplacian, Neumann Condition.Abstract
We study the existence of three weak solutions for the class of nonlinear fractional elliptic problem.
Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Amar Pal Verma
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023-12-18
Published 2024-07-01
References
G. Barles, E. Chasseigne, C. Georgelin and E. R. Jakobsen, On Neumann type problems for nonlocal equations set in a half space, Trans. Amer. Math. Soc., 366 (2014), 4873 - 4917.
K. Bogdan, K. Burdzy and Z. Q. Chen, Censored stable processes, Probab. Theory Related Fields, 127 (2003), 89 - 152.
C. Bucur and E. Valdinoci, Nonlocal Diffusion and Applications, Springer International Publishing Switzerland, 2016.
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl. (9) 86 (2006), 271 - 291.
C. Cortazar, M. Elgueta, J. D. Rossi and N. Wolanski, Boundary fluxes for nonlocal diffusion, J. Differential Equations, 234 (2007), 360 - 390.
F. Demengel and G. Demengel, Functional Spaces for the Theory of Elliptic Partial Differential Equations, Universitext, Springer London, London, 2012.
E. DiNezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. math., 136 (2012), 521 - 573.
S. Dipierro, X. Ros-Oton and E. Valdinoci, Nonlocal problems with Neumann boundary conditions, Rev. Mat. Iberoam., 33 (2017), 377 - 416.
G. Molica Bisci, V. R˘adulescu and R. Servadei, Variational Methods for Nonlocal Fractional Problems, University Printing House, Cambridge CB2 8BS, U. K., 2016.
E. Montefusco, B. Pellacci and G. Verzini, Fractional diffusion with Neumann boundary conditions: the logistic equation, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), no. 8, 2175 - 2202.
B. Ricceri, Three solutions for a Neumann problem, Topol. Methods Nonlinear Anal., 20(2) (2002), 275 - 281.
R. Servadei and E. Valdinoci, Mountain pass solutions for non-local elliptic operators, J. Math. Anal. Appl., 389 (2012), 887 - 898.
R. Servadei, E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by nonlocal operators, Rev. Mat. Iberoam, 29 (3) (2013), 1091 - 1126.
E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. III, Springer–Verlag, 1985.