Existence results to Steklov system involving the (p, q)-Laplacian
Resumen
In this paper, a quasilinear elliptic system involving a pair of (p,q)-Laplacian operators with Steklov boundary value conditions is studied. Using the Mountain Pass Geometry, we prove the existence of at least one weak solution. For the infinitely many weak solutions, we based on Bratsch’s Fountain Theorem.
Descargas
Citas
S. Aizicovici, N. S. Papageorgiou and V. Staicu, Existence and multiplicity of solutions for resonant nonlinear Neumann problems, Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 35, (2010), 235-252.
M. Allaoui, A. R. El amrouss, A. Ourraoui, Existence and multiplicity of solutions for a steklov problem, Journal of Advanced Research in Dynamical and Control Systems, Vol. 5 Issue 3, p47, (2013).
A. Ambrosetti, P. Rabinowitz, Dual variational methods in critical point theory and applications. J. Funct. Anal., 1973, 14: 349-381. https://doi.org/10.1016/0022-1236(73)90051-7
C. Atkinson and C. R. Champion, On some Boundary Value Problems for the equation ∇.(F(|∇w|)∇w) = 0, Proc.Roy.Soc.London A, 448(1995), 269-279. https://doi.org/10.1098/rspa.1995.0016
L. Boccardo and D. G. de Figueiredo, Some remarks on a system of quasilinear elliptic equations. NoDEA Nonlinear Differential Equations and Appl.,9(3)(2002), 309-323. https://doi.org/10.1007/s00030-002-8130-0
M. M. Boureanu, D. N. Udrea Existence and multiplicity results for elliptic problems with p(.) − Growth conditions, Nonlinear Analysis: Real World Applications 14 (2013) 1829-1844. https://doi.org/10.1016/j.nonrwa.2012.12.001
M. M. Boureanu, F. Preda Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions Nonlinear Differ. Equ. Appl. 19 (2012), 235-251. https://doi.org/10.1007/s00030-011-0126-1
Y. Bozhkov, E. Mitidieri, Existence of multiple solutions for quasilinear systems via bering method, J. Differential Equations ,190(2003), 239-267. https://doi.org/10.1016/S0022-0396(02)00112-2
T. Bratsch, Infinitely many solutions of a symmetric Dirirchlet problem, Nonlinear Anal. 20 (1993): 1205-1216. https://doi.org/10.1016/0362-546X(93)90151-H
S. G. Deng, Positive slutions for Robin problem involving the p(x)-Laplacian, J. Math. Anal. 360 (2009) 548-560. https://doi.org/10.1016/j.jmaa.2009.06.032
F. O. V. Depaiva, Positive and solutions for quasilinear problems, IMECC - UNICAMP, Caixa Postal 6065. 13081-970 Campinas-SP, Brazil.
A. El Hamidi, Existence results to elliptic systems with nonstandard growth conditions. Journal of Mathematical Analysis and Applications 300.1 (2004): 30-42. https://doi.org/10.1016/j.jmaa.2004.05.041
X.L. Fan, D. Zaho, On the space Lp(x) (Ω) and W m,p(x) (Ω), J. Math. Anal. Appl. 263 (2001) 424-446. https://doi.org/10.1006/jmaa.2000.7617
Y. Jabri, The Mountain Pass Theorem. Variants, Generalizations and Some Applications, Cambridge University Press, 2003. https://doi.org/10.1017/CBO9780511546655
V. K. Le; On a sub-supersolution method for variational inequalities with Leary-Liones operator in variable exponent spaces, Nonlinear Anal., 71(2009) pp. 3305-3321. https://doi.org/10.1016/j.na.2009.01.211
C. Li, C. L. Tang, Three solutions for a class of quasilinear elliptic systems involving the (p,q)-Laplacian, Nonlinear Anal.,69 (2008), 3322-3329. https://doi.org/10.1016/j.na.2007.09.021
P. Pucci, V. Radulescu, ˘ The impact of the mountain pass theory in nonlinear analysis: a mathematical survey, Boll. Unione Mat. Ital. (9) 3 (2010) 543-584.
N. M. Stavrakakis N. B. Zographopoulos* Existence results for quasilinear elliptic systems in RN∗ Electronic Journal of Differential Equations , Vol. 1999(1999), No. 39, pp. 1-15.
M. Willem, Minimax Theorems, Birkhauser, Boston, 1996. https://doi.org/10.1007/978-1-4612-4146-1
L. Zhao, P. Zhao, X. Xie, Existence and multiplicity of solutions for divergence type elliptic equations, Electron. J. Differential Equations 2011 (43) (2011) 1-9.
J. F. Zhao, Structure Theory of Banach Spaces, Wuhan University Press, Wuhan, 1991 (in Chinese).
Derechos de autor 2022 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
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).
