Existence of solutions to elliptic equations on compact Riemannian manifolds
Resumen
The aim of this paper is to investigate the existence of weak solutions of a nonlinear elliptic problem with Dirichlet boundary value condition, in the framework of Sobolev spaces on compact Riemannian manifolds
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A. Abbassi, C. Allalou and A. Kassidi, Existence of Weak Solutions for Nonlinear p-Elliptic Problem by Topological Degree, Nonlinear Dynamics and Systems Theory, 20 (3) (2020) 229–241.
T. Aubin, Problemes isopérimétriques et espaces de Sobolev. Journal of differential geometry, 11(4),(1976), 573-598.
T. Aubin, Nonlinear analysis on manifolds. Monge-Ampere equations (Vol. 252) (2012). Springer Science and Business Media.
A.Abnoune, E.Azroul and M.T.K.Abbassi: Study of a Second-Order Nonlinear Elliptic Problem Generated by a Divergence Type Operator on a Compact Riemannian Manifold, November 2018. Filomat Vol 32, No 14 (2018)(14):4811-4820.
A.Abnoune and A.Azroul, Quasi Linear Elliptic Equations with Data in L1 on Riemannian Manifold. January 2019.
M. V. Abdelkadery and A. Ourraouiz, Existence And Uniqueness Of Weak Solution For p-Laplacian Problem In RN, Appl. Math. E-Notes, 13 (2013), 228–233.
A.Bensoussan, L. Boccardo, and F. Murat, On a non linear partial differential equation having natural growth terms and unbounded solution. 5(4),(1988), 347-364.
H. Bouaam, M. El Ouaarabi, C. Allalou and S. Melliani, Variable exponent q(m)-Kirchhoff-type problems with nonlocal terms and logarithmic nonlinearity on compact Riemannian manifolds. Bulletin of the Malaysian Mathematical Sciences Society,(2023) 46(3), 97.
H. Bouaam, M. El Ouaarabi, C. Allalou, Nonlocal Kirchhoff-type problem involving variable exponent and logarithmic nonlinearity on compact Riemannian manifolds. Anal.Math.Phys. 13, 48 (2023). https://doi.org/10.1007/s13324-023-00810-0.
L. Boccardo and B. Daccorogna. A characterization of pseudo-monotone differential operators in divergence form, comm in partial diff equations 9 (11) (1984), 1107-1117.
L. Boccardo, T. Gallouët, Nonlinear elliptic equations with right-hand side measures, Comm. Partial Diferential Equations, no. 3-4, 17 (1992), 641-655.
P. Drabek and F. Nicolosi, Existence of bounded solutions for some degenerated quasilinear elliptic equations, Ann. Mat. Pura Appl. (4) 165 (1993), 217–238.
D. M. Duc and N. T. Vu, Nonuniformly elliptic equations of p-Laplacian type, Nonlinear Analysis 61 (2005).
D. M. Duc, Nonlinear singular elliptic equations, J. London Math. Soc. 40 (2) (1989).
E. Hebey, Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities, Courant Lecture Notes, vol. 5, American Mathematical Society, 2000.
E. Hebey, Introduction l’analyse non linaire sur les variétès. Ed. Diderot (1997).
E. Hebey, Sobolev spaces on Riemannian manifolds, Springer lect. Notes in Mth. 1635 .
El Ouaarabi, M., Allalou, C., Melliani, S.: On a class of p(x)-Laplacian-like Dirichlet problem depending on three real parameters. Arab. J. Math. 11(2), 227–239 (2022)/
El Ouaarabi, M., Allalou, C., Melliani, S.: Weak solution of a Neumann boundary value problem with p(x)-Laplacianlike operator. Analysis. 42(4), 271–280 (2022).
El Ouaarabi, M., Allalou, C., Melliani, S.: Existence result for Neumann problems with p(x)-Laplacian-like operators in generalized Sobolev spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 1337–1350 (2023).
El Ouaarabi, M., Allalou, C., Melliani, S.: Existence of weak solution for a class of p(x)-Laplacian problems depending on three real parameters with Dirichlet condition. Bol. Soc. Mat. Mex. 28, 31(2022).
P. Lindqvist, On the equation ∇p(u) + |u|p−2u = 0. Proc. Amer. Math. Soc. Vol.109, no. (1990), 157-164.
S. Liu, Existence of solutions to a superlinear p-Laplacian equation. (2001) 49J35, 35J65, 35B34.
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