Weak solution to p(x)-Kirchoff type problems under no-flux boundary condition by topological degree
Resumo
This paper is concerned with the existence of weak solutions of $p(x)$-Kirchhoff type problems with no-flux boundary condition. Our technical approach is based on topological degre methods of Berkovits.
Downloads
Referências
C. Allalou, M. El Ouaarabi, S. Melliani ” Existence and uniqueness results for a class of p(x)-Kirchhoff-type problems with convection term and Neumann boundary data. J Elliptic Parabol Equ (2022). DOI: https://doi.org/10.1007/s41808-022-00165-w
Y. Akdim, E. Azroul and A. Benkirane, Existence of solutions for quasilinear degenerate elliptic equations. Electronic Journal of Differential Equations (EJDE), 2001, vol. 2001, p. Paper No. 71, 19.
J .Berkovits, on the degree theory for nonlineair mapping of monotone type, Vol 58. Helsinki: Guomalaimen Tiedeakatemia, 1986. DOI: https://doi.org/10.1016/0024-3795(86)90317-4
M. M. Boureanu and D. Udrea, Existence and multiplicity results for elliptic problems with p(x)-growth conditions, Nonlinear Anal. Real World Appl., 14(2013), 1829-1844. DOI: https://doi.org/10.1016/j.nonrwa.2012.12.001
J. Berkovits, Extension of the Leray-Schauder degree for abstract Hammerstein type mappings. Journal of Differential Equations, 2007, vol. 234, no 1, p. 289-310. DOI: https://doi.org/10.1016/j.jde.2006.11.012
F. E. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. (N.S.), 9 (1983), 1-39. DOI: https://doi.org/10.1090/S0273-0979-1983-15153-4
E. Cabanillas, A. G. Aliaga, W. Barahona and G. Rodriguez, Existence of solutions for a class of p (x)-Kirchhoff type equation viatopological methods. J. Adv. Appl. Math. and Mech 2.4 (2015): 64-72.
E. Cabanillas, J. B. B. Barros, R. J. de la Cruz Marcacuzco and Z. H. Segura, Existence of Solutions for a Class of p(x)−Kirchhoff Type Equation with Dependence on the Gradient.” Kyungpook Mathematical Journal 58.3 (2018): 533-546.
S. Heidarkhani, G. A. Afrouzi, J. Henderson, S. Moradi and G. Caristi, Variational approaches to p-Laplacian discrete problems of Kirchhoff-type. Journal of Difference Equations and Applications 23.5 (2017): 917-938. DOI: https://doi.org/10.1080/10236198.2017.1306061
M. Chipot and J. F. Rodrigues, On a class of nonlocal nonlinear elliptic problems, RAIRO, ModA©lisation ˜ Mathematique et Analyse Numerique, 26(1992) 447-467. DOI: https://doi.org/10.1051/m2an/1992260304471
M. Mihailescu, On a class of nonlinear problems involving a p(x)-Laplace type operator, Czechoslovak Math. J. 58 (2008) 155-172. DOI: https://doi.org/10.1007/s10587-008-0011-1
H. Fan, Multiple positive solutions for a class of Kirchho¨ı¬€ type problems involving critical Sobolev exponents, J. Math.Anal. Appl. 431 (2015) 150-168. DOI: https://doi.org/10.1016/j.jmaa.2015.05.053
X.L. Fan ,D. Zhao On the Spaces Lp(x) (Ω) and W m,p(x) (Ω). J Math Anal Appl. 2001;263:424-446. DOI: https://doi.org/10.1006/jmaa.2000.7617
F. Faraci and C. Farkas. On a critical Kirchhoff-type problem. Nonlinear Analysis 192 (2020): 111679. DOI: https://doi.org/10.1016/j.na.2019.111679
S. Kichenassamy, L. Veron, Singular solutions of the p-Laplace equation,Math. Ann. 275 (1985) 599-615. DOI: https://doi.org/10.1007/BF01459140
G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883
O. Kovacik , J.Rakosnık . On spaces Lp(x) and W1,p(x) . Czechoslovak Math. J. 1991;41(4):592-618. DOI: https://doi.org/10.21136/CMJ.1991.102493
J. Leray, J. Schauder, Topologie et equations fonctionnelles, Ann. Sci. Ec. Norm., 51 (1934), 45-78. DOI: https://doi.org/10.24033/asens.836
S. A Temghart, A.Kassidi, C.Allalou, A. Abbassi. On an elliptic equation of Kirchhoff type problem via topological degree. Nonlinear Studies, 28 (4), (2021), 1179-1193.
S. Yacini, C. Allalou, K. Hilal, and A. Kassidi: Weak solutions to kirchhoff type problems via topological degree. Advanced Mathematical Models and Applications Vol.6, No.3, 2021, pp.309-321.
Z. Yucedag and R. Ayazoglu. Existence of solutions for a class of Kirchhoff-type equation with nonstandard growth. Univ. J. App. Math 2.5 (2014): 215-221. DOI: https://doi.org/10.13189/ujam.2014.020504
E. Zeider, Nonlinear Functional Analysis and its Applications, IIB : Nonlinear Monotone Operators, Springer, New York, 1990.
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
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).
