Steklov problems for the p−Laplace operator involving Lq-norm
References
- [1] A. Anane, Simplicit et isolation de la premiere valeur propre du p-laplacien avec poids, C. R. Acad. Sci. Paris Ser. I Math. 305, no. 16 (1987), 725-728.
- [2] A. Anane, O. Chakrone, N. Moradi, Regularity of the solutions to a nonlinear boundary problem with indefinite weight, Bol. Soc. Paran. Mat. V. 29, no. 1 (2011), 17-23.
- [3] A. Anane and N. Tsouli, On the second eigenvalue of the p-Laplacian, in: Nonlinear partial differential equations (Fs, 1994), Pitman Res. Notes Math. Ser. 343, Longman, Harlow, 1996, pp. 1-9.
- [4] L. Brasco, G. Franzina, Convexity properties of Dirichlet integrals and Picone type inequalities, Kodai Math. J., 37 (2014), 769-799.10.2996/kmj/1414674621
- [5] J. I. Diaz, Nonlinear partial differential equations and free boundaries, Vol. I, Elliptic Equations, London, (1985)
- [6] E. DiBenedetto, C1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7(8) (1983), 827-850.10.1016/0362-546X(83)90061-5
- [7] P. Drabek, A. Kufner and F. Nicolosi, Quasilinear elliptic equations with degenerations and singularities, de Gruyter Series in Nonlinear Analysis and Applications, vol. 5, Walter de Gruyter and Co., Berlin, (1997)10.1515/9783110804775
- [8] A. El Khalil and M. Ouanan, Boundary eigencurve problems involving the p-laplace operator, Electronic Journal of Differential Equations, Vol 2008, No. 78 (2008), 1-13.
- [9] A. El Khalil and A. Touzani, On the first eigencurve of the p-Laplacian, Partial Differential Equations, Lecture Notes in Pure and Applied Mathematics Series 229, Marcel Dekker, Inc. (2002), 195-205.10.1201/9780203910108.ch16
- [10] J. Fernández Bonder and J. D. Rossi, A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding, Publ. Mat. 46 (1) (2002), 221-235.10.5565/PUBLMAT_46102_12
- [11] J. P. Garcia Azorero and I. Peral Alonso, Existence and nonuniqueness for the p-Laplacian: nonlinear eigenvalues, Communications in Partial Differential Equation 12 (1987), 1389-1430.10.1080/03605308708820534
- [12] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second order, Springer, Berlin, (1983)
- [13] B. Kawohl and P. Lindqvist, Positive eigenfunctions for the p-Laplace operator revisited, Analysis (Munich), 26 (2006), 545-550.
- [14] B. Kawohl, M. Lucia and S. Prashanth, Simplicity of the principal eigenvalue for indefinite quasilinear problems, Adv. Differential Equations, 12 (4)(2007), 407-434.10.57262/ade/1355867457
- [15] A. Le, emph Eigenvalue problems for the p-Laplacian, Nonlinear Analysis 64 (2006), 1057-1099.10.1016/j.na.2005.05.056
- [16] P. Lindqvist, On the equation div(|∇u|p−2∇u) + λ|u|p−2u = 0, Proceedings of the Amirican American Mathematical Society 109 (1990), 157-164.
- [17] M.Ôtani and T. Teshima, On the first eigenvalue of some quasilinear elliptic equations, Proc. Japan Acad., Ser. A Math. Sci., 64 (1988), 8-10.
- [18] M. W. Steklov, Sur les problemes fondamentaux de la physique mathematique, Ann. Sci. Ecole Norm 19, (1902), 445-490.10.24033/asens.516
- [19] A. Szulkin, Ljusternik-Schnirelmann theory on C1-manifolds, Ann. Inst. Henri Poincaré, Anal., 5 (1988),119-139.
- [20] P. Tolksdorf, Regularity for a more general class of quasilinearelliptic equations, Electronic Journal of Differential Equations, 51(1) (1984), 126-150.10.1016/0022-0396(84)90105-0
- [21] O. Torn, Steklov problem with an indefinite weight for the p-Laplacien, Electronic Journal of Differential Equations, Vol. 2005, No. 87 (2005), 1-8.
- [22] J. L. Vazquez, A Strong Maximum Principle for Some Quasilinear Elliptic Equations, Appl. Math. Optim., 12 (1984), 191-202.10.1007/BF01449041
- [23] A. Zerouali B. Karim, A. Anane and O. Chakrone, Two-Parameter Eigenvalues Steklov Problem involving the p-Laplacian, Advances in Dynamical Systems and Applications ISSN 0973-5321, Volume 8, Number 1 (2013), pp. 149-156
DOI: https://doi.org/10.2478/mjpaa-2022-0016 | Journal eISSN: 2351-8227
Language: English
Page range: 228 - 243
Submitted on: Sep 17, 2021
Accepted on: Feb 22, 2022
Published on: May 28, 2022
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year
Keywords:
Related subjects:
© 2022 My Driss Morchid Alaoui, Abdelouahd El Khalil, Abdelfattah Touzani, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.