Topological degree methods for a Neumann problem governed by nonlinear elliptic equation

[1] A. Abbassi, E. Azroul, A. Barbara, Degenerate p(x)-elliptic equation with second membre in L¹. Advances in Science, Technology and Engineering Systems Journal. Vol. 2, No. 5 (2017), 45-54.10.25046/aj020509Search in Google Scholar

[2] A. Abbassi, C. Allalou and A. Kassidi, Existence of weak solutions for nonlinear p-elliptic problem by topological degree, Nonlinear Dyn. Syst. Theory, 20(3) (2020) 229-241.10.1007/s41808-021-00098-wSearch in Google Scholar

[3] S. Aizicovici, N.S. Papageorgiou, V. Staicu, Nodal solutions for nonlinear nonhomogeneous Neumann equations, Topol. Methods Nonlinear Anal. 43 (2014) 421-438.10.12775/TMNA.2014.025Search in Google Scholar

[4] 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.Search in Google Scholar

[5] C. Atkinson and C. R. Champion, Some boundary value problems for the equation ∇.(| ∇ ϕ |^N∇ ϕ) = 0, Quart. J. lllcch. Appl. Math. 37 (1984), 401-419.10.1093/qjmam/37.3.401Search in Google Scholar

[6] C. Atkinson and C. W. Jones, Similarity solutions in some non-linear diffusion problems and in boundary-layer flow of a pseudo plastic fluid, Quart. J. Mech. Appl. Malh. 27 (1974), 193-211.10.1093/qjmam/27.2.193Search in Google Scholar

[7] J. Baranger and K. Najib, Numerical analysis for quasi-Newtonian flow obeying the power Iaw or the Carreau law, Numer. Math. 58 (1990), 35-49.10.1007/BF01385609Search in Google Scholar

[8] J. Berkovits, Extension of the LeraySchauder degree for abstract Hammerstein type mappings. Journal of Differential Equations, 2007, vol. 234, no 1, p. 289-310.10.1016/j.jde.2006.11.012Search in Google Scholar

[9] G. Bonanno, G. D’Agui and A. Sciammetta. Nonlinear elliptic equations involving the p-laplacian with mixed Dirichlet-Neumann boundary conditions. Opuscula Mathematica, 2019, vol. 39, no 2.10.7494/OpMath.2019.39.2.159Search in Google Scholar

[10] F. E. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. (N.S.), 9 (1983), 1-39.10.1090/S0273-0979-1983-15153-4Search in Google Scholar

[11] Y.J. Cho, and Y. Q. Chen. Topological degree theory and applications. Chapman and Hall/CRC, 2006.10.1201/9781420011487Search in Google Scholar

[12] P. Drabek, A. Kufner and F. Nicolosi, Non Linear Elliptic Equations, Singular and Degenerated Cases. University of West Bohemia, 1996.Search in Google Scholar

[13] P. Drabek, A. Kufner and V. Mustonen, Pseudo-monotonicity and degenerate or singular elliptic operators, Bull. Austral. Math. Soc. Vol. 58 (1998), 213-221.10.1017/S0004972700032184Search in Google Scholar

[14] M. Filippakis, N.S. Papageorgiou, Nodal solutions for Neumann problems with a nonhomogeneous differential operator, Funkcial. Ekvac. 56 (2013) 63-79.10.1619/fesi.56.63Search in Google Scholar

[15] J. P. Garca Azorero, and I. Peral Alonso, Existence and nonuniqueness for the p-Laplacian, Communications in Partial Differential Equations 12.12 (1987): 126-202.10.1080/03605308708820534Search in Google Scholar

[16] L. Gasiński, N.S. Papageorgiou, Multiple solutions for a class of nonlinear Neumann eigenvalue problems, Commun. Pure Appl. Anal. 13 (2014) 1491-151210.3934/cpaa.2014.13.1491Search in Google Scholar

[17] M. A. Hammou, E. Azroul and B. Lahmi, Existence of solutions for p(x)-Laplacian Dirichlet problem by topological degree, Bulletin of the Transilvania University of Brasov ffl Vol 11(60), No. 2-2018, Series III: Mathematics, Informatics, Physics, 29-38.Search in Google Scholar

[18] M. A. Hammou, E. Azroul and B. Lahmi, Topological degree methods for a Strongly nonlinear p(x)-elliptic problem. Revista Colombiana de Matemticas 53.1 (2019): 27-39.10.15446/recolma.v53n1.81036Search in Google Scholar

[19] A. Hirn, Approximation of the p-Stokes equations with equal-order finite elements, J. Math. Fluid Mech. 15 (2013) 65-88.10.1007/s00021-012-0095-0Search in Google Scholar

[20] S.C. Hu, N.S. Papageorgiou, Nonlinear Neumann problems with indefinite potential and concave terms, Commun. Pure Appl. Anal. 14 (2015) 2561 – 2616.10.3934/cpaa.2015.14.2561Search in Google Scholar

[21] T. He, Z. A. Yao and Z. Sun, Multiple and nodal solutions for parametric Neumann problems with nonhomogeneous differential operator and critical growth. Journal of Mathematical Analysis and Applications, 2017, vol. 449, no 2, p. 1133-1151.10.1016/j.jmaa.2016.12.020Search in Google Scholar

[22] B. Kawohl, On a family of torsional creep problems, J. R. Angew. Math. 410 (1990) 1-22.10.1515/crll.1990.410.1Search in Google Scholar

[23] I.S. Kim, A topological degree and applications to elliptic problems with discontinuous nonlinearity, J. Nonlinear Sci. Appl. 10, 612-624 (2017).10.22436/jnsa.010.02.24Search in Google Scholar

[24] J. Leray, J. Schauder, Topologie et quations fonctionnelles, Ann. Sci. Ec. Norm., 51 (1934), 45-7810.24033/asens.836Search in Google Scholar

[25] S. Liu, Existence of solutions to a superlinear p-Laplacian equation, Electron. J. Differential Equations 66.6 (2001).Search in Google Scholar

[26] Z. Liu, D. Motreanu, and S. Zeng. Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient. Calculus of Variations and Partial Differential Equations 58.1 (2019): 28.10.1007/s00526-018-1472-1Search in Google Scholar

[27] S.E. Manouni, N.S. Papageorgiou, P. Winkert, Parametric nonlinear nonhomogeneous Neumann equations involving a nonhomogeneous differential operator, Monatsh. Math. 177 (2015) 203-233.10.1007/s00605-014-0649-8Search in Google Scholar

[28] D. Motreanu, V. V. Motreanu and N. Papageorgiou, Topological and variational methods with applications to nonlinear boundary value problems. Vol. 1. No. 7. New York: Springer, 2014.10.1007/978-1-4614-9323-5Search in Google Scholar

[29] J. R. Philip, N-diffusion, Aust. J. Phiys. 14 (1961), 1-13.10.1071/PH610001Search in Google Scholar

[30] M. Sabouri and M. Dehghan. A hk mortar spectral element method for the p-Laplacian equation. Computers and Mathematics with Applications 76.7 (2018): 1803-1826.10.1016/j.camwa.2018.07.031Search in Google Scholar

[31] I. V. Skrypnik, Methods for analysis of nonlinear elliptic boundary value problems, Translated from the 1990 Russian original by Dan D. Pascali, Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, (1994).10.1090/mmono/139Search in Google Scholar

[32] I. V. Skrypnik, Nonlinear elliptic equations of higher order, (Russian) Gamoqeneb. Math. Inst. Sem. Mosen. Anotacie, 7 (1973), 51-52.Search in Google Scholar

[33] E. Zeider, Nonlinear Functional Analysis and its Applications, II\B : Nonlinear Monotone Operators, Springer, New York, 1990.Search in Google Scholar