An eigenvalue of anisotropic discrete problem with three variable exponents
Анотація
УДК 517.5
Власне значення анiзотропної дискретної задачiз трьома змiнними експонентами
Вивчається проблема iснування неперервного спектра анiзотропної дискретної задачi iз змiнною експонентою.
Запропонований пiдхiд базується на варiацiйних методах та теорiї критичних точок.
Посилання
R. P. Agarwal, K. Perera, D. O’Regan, Multiple positive solutions of singular and nonsingular discrete problems via variational methods, Nonlinear Anal., 58, no. 1-2, 69 – 73 (2004), https://doi.org/10.1016/j.na.2003.11.012 DOI: https://doi.org/10.1016/j.na.2003.11.012
R. P. Agarwal, K. Perera, D. O’Regan, Multiple positive solutions of singular $p$-Laplacian discrete problems via variational methods, Adv. Difference Equat. 2005, № 2, 93 – 99 (2009), https://doi.org/10.1155/ade.2005.93 DOI: https://doi.org/10.1155/ADE.2005.93
A. Cabada, A. Iannizzotto, S. Tersian, Multiple solutions for discrete boundary-value problems, J. Math. Anal. and Appl., 356, no. 2, 418 – 428 (2009), https://doi.org/10.1016/j.jmaa.2009.02.038 DOI: https://doi.org/10.1016/j.jmaa.2009.02.038
G. Bonanno, P. Candito, Infinitely many solutions for a class of discrete nonlinear boundary-value problems, Appl. Anal., 88, no. 4, 605 – 616 (2009), https://doi.org/10.1080/00036810902942242 DOI: https://doi.org/10.1080/00036810902942242
G. Bonanno, P. Candito, G. D´agui, Variational methods on finite dimensional Banach spaces and discrete problems, Adv. Nonlinear Stud., 14, no. 4, 915 – 939 (2014), https://doi.org/10.1515/ans-2014-0406 DOI: https://doi.org/10.1515/ans-2014-0406
G. Bonanno, G. D´agui, Two non-zero solutions for elliptic Dirichlet problems, Z. Anal. und Anwend., 35, no. 4, 449 – 464 (2016), https://doi.org/10.4171/ZAA/1573 DOI: https://doi.org/10.4171/ZAA/1573
M. Galewski, R. Wieteska, Existence and multiplicity results for boundary-value problems connected with the discrete $p(cdot)$-Laplacian on weighted finite graphs, Appl. Math. and Comput., 290, 376 – 391 (2016), https://doi.org/10.1016/j.amc.2016.06.016 DOI: https://doi.org/10.1016/j.amc.2016.06.016
M. Galewski, R. Wieteska, On the system of anisotropic discrete BVPs, J. Difference Equat. and Appl., 19, № 7, 1065 – 1081 (2013), https://doi.org/10.1080/10236198.2012.709508 DOI: https://doi.org/10.1080/10236198.2012.709508
M. Galewski, R. Wieteska, Existence and multiplicity of positive solutions for discrete anisotropic equations, Turkish J. Math., 38, no. 2, 297 – 310 (2014), https://doi.org/10.3906/mat-1303-6 DOI: https://doi.org/10.3906/mat-1303-6
M. Galewski, R. Wieteska, Positive solutions for anisotropic discrete boundary-value problems, Electron. J. Different. Equat. and Appl., 2013, № 32, 1 – 9 (2013).
M. Galewski, Sz. Glab, On the discrete boundary-value problem for anisotropic equation, J. Math. Anal. and Appl., 386, № 2, 956 – 965 (2012), https://doi.org/10.1016/j.jmaa.2011.08.053 DOI: https://doi.org/10.1016/j.jmaa.2011.08.053
M. Galewski, G. Molica Bisci, R. Wieteska, Existence and multiplicity of solutions to discrete inclusions with the $p(k)$-Laplacian problem, J. Difference Equat. and Appl., 21, № 10, 887 – 903 (2015), https://doi.org/10.1080/10236198.2015.1056177 DOI: https://doi.org/10.1080/10236198.2015.1056177
B. Kone, S. Ouaro, Weak solutions for anisotropic discrete boundary-value problems, J. Difference Equat. and Appl., 16, № 10, 1 – 11 (2010), https://doi.org/10.1080/10236191003657246
M. Khaleghi Moghadam, J. Henderson, Triple solutions for a dirichlet boundary-value problem involving a perturbed discrete $p(k)$-Laplacian operator, Open Math., 15, № 1, 1075 – 1089 (2017). DOI: https://doi.org/10.1515/math-2017-0090
M. Khaleghi Moghadam, M. Avci, Existence results to a nonlinear $p(k)$-Laplacian difference equation, J. Difference Equat. and Appl., 23, № 10, 1652 – 1669 (2017), https://doi.org/10.1080/10236198.2017.1354991 DOI: https://doi.org/10.1080/10236198.2017.1354991
B. Kone, S. Ouaro, Weak solutions for anisotropic discrete boundary-value problems, J. Difference Equat. and Appl., 17, № 10, 1537 – 1547 (2011), https://doi.org/10.1080/10236191003657246 DOI: https://doi.org/10.1080/10236191003657246
A. Kristaly, M. Mih˘ailescu, V. R˘adulescu, S. Tersian, Spectral estimates for a nonhomogeneous difference problem, Commun. Contemp. Math., 12, 1015 – 1029 (2010), https://doi.org/10.1080/10236191003657246 DOI: https://doi.org/10.1142/S0219199710004093
G. Molica Bisci, D. Repovš, Existence of solutions for $p$-Laplacian discrete equations, Appl. Math. and Comput., 242, 454 – 461 (2014), https://doi.org/10.1016/j.amc.2014.05.118 DOI: https://doi.org/10.1016/j.amc.2014.05.118
G. Molica Bisci, D. Repovs, On sequences of solutions for discrete anisotropic equations, Expo. Math., 32, no. 3, 284 – 295 (2014), https://doi.org/10.1016/j.exmath.2013.12.001 DOI: https://doi.org/10.1016/j.exmath.2013.12.001
M. Mihăilescu, V.Rădulescu, S. Tersian, Eigenvalue problems for anisotropic discrete boundary-value problems, J. Difference Equat. and Appl., 15, no. 6, 557 – 567 (2009), https://doi.org/10.1080/10236190802214977 DOI: https://doi.org/10.1080/10236190802214977
J. Smejda, R. Wieteska, On the dependence on parameters for second order discrete boundary-value problems with the $p(k)$-Laplacian, Opuscula Math., 34, no. 4, 851 – 870 (2014), https://doi.org/10.7494/OpMath.2014.34.4.851 DOI: https://doi.org/10.7494/OpMath.2014.34.4.851
M. Struwe, Variational methods, applications to nonlinear partial differential equations and Hamiltonian systems, Springer-Verlag, Berlin (1986), https://doi.org/10.1007/978-3-662-02624-3 DOI: https://doi.org/10.1007/978-3-662-02624-3
Для цієї роботи діють умови ліцензії Creative Commons Attribution 4.0 International License.
