Weak solution for perturbed fractional p-Laplacian system via Young measures
Resumen
In this work, we demonstrate the existence of weak solutions to a class of fractional p-Laplacian problems in degenerate form. Under appropriate assumptions concerning the main functions, the existence of weak solutions is obtained by applying the Galerkin method combined with the theory of Young measures.
Descargas
Citas
A. Abassi, A. El Hachimi, A. Jamea, Entropy solutions to nonlinear Neumann problems with L1-data, International Journal of Mathematics and Statistics 2 (2008), no. S08, 4-17.
E. Azroul and F. Balaadich, Weak solutions for generalized p-Laplacian systems via Young measures, Moroccan Journal of Pure and Applied Analysis, 4(2):77-84, 2018. https://doi.org/10.1515/mjpaa-2018-0008.
F. Balaadich and E. Azroul, Existence results for fractional p-Laplacian systems via Young measures, Math. Model. Anal., 27 (2022), no. 2, 232-241.
F. Balaadich, E. Azroul, Generalized p-Laplacian systems with lower order terms, Int. J. Nonlinear Anal. Appl. 13 (2022) No. 1, 45-55 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2021.20666.2191
F. Balaadich and E. Azroul, Elliptic systems of p-Laplacian type, Tamkang Journal of Mathematics Volume 53, Number 1, 11-21, March 2022 https://10.5556/j.tkjm.53.2022.3296.
J. M. Ball. A version of the fundamental theorem for Young measures, In PDEs and continuum models of phase transitions, volume 344, pp. 207-215. Springer, Springer, Berlin, Heidelberg, 1989. https://doi.org/10.1007/BFb0024945.
G. Benhamida, T. Moussaoui and D. O’Regan, Existence and uniqueness of solutions for fractional p-Laplacian problem in RN, Discuss. Math. DICO 38 (2018) 5-14. https://10.7151/dmdico.1201.
L. Brasco, E. Lindgren and E. Parini, The fractional Cheeger problem, Interfaces Free Boundaries 16 (2014), no. 3, 419-458.
L. C. Evans, Weak convergence methods for nonlinear partial differential equations, Volume 74. American Mathematical Society, 1990. https://doi.org/10.1090/cbms/074.
A. Fiscella, R. Servadei, and E. Valdinoci, Density properties for fractional Sobolev spaces, Ann. Acad. Sci. Fenn. Math. 40 (2015), no. 1, 235-253.
N. Hungerb¨uhler, A refinement of Balls theorem on Young measures. New York Journal of Mathematics, 3:48-53, 1997.
A. Iannizzotto and M. Squassina, 1/2-Laplacian problems with exponential non- linearity, Journal of Mathematical Analysis and Applications, 414(1):372-385, 2014. https://doi.org/10.1016/j.jmaa.2013.12.059.
A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, volume 204. Elsevier, 2006.
J. L. Lions, Quelques m´ethodes de r´esolution de probl`emes aux limites non lin´eaires . Etudes math´ematiques, 1969.
E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. Math. 136 (2012) 521-573. doi:10.1016/j.bulsci.2011.12.004.
P. Pucciand, R. Servadei, On weak solutions for p-Laplacian equations with weights, Rend. Lincei Mat. Appl. 18 (2007), 257-267.
H. Qiu and M. Xiang, Existence of solutions for fractional p-Laplacian problems via Leray-Schauder’s nonlinear alternative, Boundary Value Problems, 83:1-8, 2016. https://doi.org/10.1186/s13661-016-0593-8.
W. Rudin, Real and complex analysis, McGraw-Hill Book Company, New York, NY, 1966.
A. Sabri, H. T. Alaoui and A. Jamea, Existence of weak solution for fractional p-Laplacian problem with Dirichlet-type boundary condition, Discussiones Mathematicae Differential Inclusions, Control and Optimization 39 (2019) 69-80 doi:10.7151/dmdico.1211.
R. Servadei and E. Valdinoci, Mountain Pass solutions for non-local elliptic operators, Journal of Mathematical Analysis and Applications, 389(2):887-898, 2012. https://doi.org/10.1016/j.jmaa.2011.12.032.
R. Servadei and E. Valdinoci, Weak and viscosity solutions of the fractional Laplace equation, Publ. Mat. 58 (2014) 133-154. doi:10.5565/publmat-58114-06.
M. Xiang, B. Zhang and M. Ferrara, Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian, Journal of Mathematical Analysis and Applications, 424(2):1021-1041, 2015. https://doi.org/10.1016/j.jmaa.2014.11.055.
J. Xu, D. O’Regan and W. Dong, Existence of weak solutions for a fractional p-Laplacian equation in RN , Sci. China Math. 111 (2017) 1647-1660.
E. Zeidler, Nonlinear functional analysis and its application, volume I. Springer, 1986.
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
