Nonlinear equations with a generalized fractional Laplacian-Reference-Cited by-同舟云学术

Nonlinear equations with a generalized fractional Laplacian

Published:2021-01-23 Issue:2 Volume:115 Page:
ISSN:1578-7303
Container-title:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
language:en
Short-container-title:RACSAM

Author:

Kossowski Igor^ORCID,Przeradzki Bogdan

Abstract

AbstractWe study a generalization of the power of Laplace operator with null Dirichlet conditions by means of the spectral theory and prove several existence results for nonlinear equations with such operators, especially when the problem is resonant. Some regularity results are also obtained.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s13398-021-00998-5.pdf

Reference27 articles.

1. Barrios, B., Colorado, E., de Pablo, A., Sánchez, U.: On some critical problems for the fractional Laplacian operator. J. Diff. Equ. 252, 6133–6162 (2012)

2. Molica Bisci, G., Radulescu, V., Servadei, R.: Variational Methods for fractional Boundary Problems. Cambridge Univ. Press, Cambridge (2016)

3. Bucur, C., Valdinoci, E.: Nonlocal diffusion and applications, Lecture Notes of the Unione Math. Italiana, 20, Springer, Bologna (2016)

4. Cabre, X., Tan, J.: Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv. Math. 224, 2052–2093 (2010)

5. Capella, A., Dávila, J., Dupaigne, L., Sire, Y.: Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations. Commun. Partial Differ. Equ. 36, 1353–1384 (2011)

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