Existence results of a nonlocal superlinear problems Involving $p(x)-$Laplacian near to zero

  • Abdelrachid El Amrouss University Mohamed I
  • Anass Ourraoui University Mohamed I

Abstract

In this work, by using a variational approach, we give a result on the existence and multiplicity of solutions concerned a class of nonlocal elliptic problems  with variable exponent.

Downloads

Download data is not yet available.

Author Biography

Anass Ourraoui, University Mohamed I

Faculté des Sciences d'Oujda

References

M. Allaoui, A. El Amrouss, A. Ourraoui, Existence results for a class of nonlocal problems involving p(x)−Laplacian, Math. Meth. Appl. Sci. 2016, 39 824-832. https://doi.org/10.1002/mma.3524

C. O. Alves, F. J. S. A. Correa, G. M. Figueiredo, On a class of nonlocal elliptic problems with critical growth, DEA 2 (2010) 409-417. https://doi.org/10.7153/dea-02-25

C. O. Alves, F. J. S. A. Correa, On existence of solutions for a class of problem involving a nonlinear operator, Comm. Appl. Nonlinear Anal. 8 (2001) 43-56.

G. Autuori, P. Pucci, M. C. Salvatori, Asymptotic stability for anisotropic Kirchhoff systems, J. Math. Anal. Appl. 352 (2009) 149-165. https://doi.org/10.1016/j.jmaa.2008.04.066

M. Avci, B. Cekic and R. A. Mashiyev, Existence and multiplicity of the solutions of the p(x)−Kirchhoff type equation via genus theory, Math. Methods Appl. Sci. 34 (14), 1751-1759. https://doi.org/10.1002/mma.1485

K. Ben Ali, A. Ghanmi, and K. Kefi, Minimax method involving singular p(x)−Kirchhoff equation, Journal of Mathematical Physics, Volume 58, Issue 11 https://doi.org/10.1063/1.5010798

M. Chipot and B. Lovat, Some remarks on nonlocal elliptic and parabolic problems, Nonlinear Anal., 30 (7) (1997), 4619-4627. https://doi.org/10.1016/S0362-546X(97)00169-7

G. Dai, Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)−Laplacian, App. Anal. (2011) 1-20.

DE. Edmunds, J. Rakosnık. Sobolev embedding with variable exponent. Studia Math. 2000; 143: 267-293. https://doi.org/10.4064/sm-143-3-267-293

X. L. Fan, D. Zhao, A class of De Giorgi type and Holder continuity, Nonlinear Anal. 36 (1999) 295-318. https://doi.org/10.1016/S0362-546X(97)00628-7

X. L. Fan, Global C1,α regularity for variable exponent elliptic equations in divergence form, J. Differential Equations 235 (2) (2007) 397-417.

X. L. Fan, On nonlocal p(x)−Laplacian Dirichlet problems, Nonlinear Anal. 72 (2010) 3314-3323. 13. X.L. Fan, D.Zhao, On the spaces Lp(x) (Ω) and W m,p(x) (Ω), J.Math.Anal.Appl, 263(2001)424-446. https://doi.org/10.1016/j.na.2009.12.012

M. G. Figueiredo, Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument, J. Math. Anal. Appl. 401 (2013) 706-713. https://doi.org/10.1016/j.jmaa.2012.12.053

H. P. Heinz, Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems, J. Differential Equations 66 (2) (1987) 263-300. https://doi.org/10.1016/0022-0396(87)90035-0

G. Kirchhok, Vorlesungen uber mathematische Physik : Mechanik, Leipzig : B.G. Teubner, 1883.

G. M Bisci, V. Radulescu, R. Servadei, Variational Methods for Nonlocal Fractional Problems, Encyclopedia of Mathematics and its Applications, vol. 162, Cambridge University Press, Cambridge, 2016.

A. Ourraoui, On an elliptic equation of p−Kirchhoff type with convection term, C.R.Acad.Sci.Paris, Ser.I 354(2016)253-256. https://doi.org/10.1016/j.crma.2015.10.025

A. Ourraoui, On Nonlocal p(x)-Laplacian problems involving No Flux boundary condition, Note Mat. 35 (2015) no. 2, 69-81.

A. Ourraoui, Multiplicity results for Steklov problem with variable exponent, Applied Mathematics and Computation 277:(2016) 34-43. https://doi.org/10.1016/j.amc.2015.12.043

M. Ruzicka , Flow of shear dependent electrorheological fluids, CR Math. Acad. Sci. Paris 329 (1999) 393-398. https://doi.org/10.1016/S0764-4442(00)88612-7

Z. Tan, F. Fang, On superlinear p(x)−Laplacian problems without Ambrosetti and Rabinowitz condition, Nonlinear Analysis 75 (2012) 3902-3915. https://doi.org/10.1016/j.na.2012.02.010

V. Zhikov, Averaging of functionals in the calculus of variations and elasticity, Math. USSR Izv. 29 (1987) 33-66. https://doi.org/10.1070/IM1987v029n01ABEH000958

Published
2022-01-30
Section
Articles