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Infinitely many solutions for a class of Dirichlet quasilinear elliptic systems. (English) Zbl 1253.34026

From the introduction: The aim of this paper is to investigate the existence of infinitely many classical solutions for the following Dirichlet quasilinear elliptic system

-(p i -1)|u i ' (x)| p i -2 u i '' (x)=λF u i (x,u 1 ,,u n )h i (x,u i ' ),x(a,b),
u i (a)=u i (b)=0,for1in,

where p i >1 for 1in, λ is a positive parameter, a,b with a<b, h i :[a,b]×[0,+) is a bounded and continuous function with m i :=inf (x,t)[a,b]× h i (x,t)>0 for 1in, F:[a,b]× n is a function such that the mapping (t 1 ,t 2 ,,t n )F(x,t 1 ,t 2 ,,t n ) is in C 1 in n for all x[a,b], F u i is continuous in [a,b]× n for 1in, where F u i denotes the partial derivative of F with respect to u i , and

sup |(t 1 ,,t n )|M |F u i (x,t 1 ,,t n )|L 1 ([a,b])

for all M>0 and all 1in.

34B15Nonlinear boundary value problems for ODE
58E50Applications of variational methods in infinite-dimensional spaces
[1]Bonanno, G.; Bisci, G. Molica: Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. value probl. 2009, 1-20 (2009) · Zbl 1177.34038 · doi:10.1155/2009/670675
[2]Bonanno, G.; D’aguì, G.: A Neumann boundary value problem for the Sturm–Liouville equation, Appl. math. Comput. 208, 318-327 (2009) · Zbl 1176.34020 · doi:10.1016/j.amc.2008.12.029
[3]Bonanno, G.; Di Bella, B.: Infinitely many solutions for a fourth-order elastic beam equation, Nodea nonlinear differential equations appl. 18, 357-368 (2011) · Zbl 1222.34023 · doi:10.1007/s00030-011-0099-0
[4]Bonanno, G.; Bisci, G. Molica: Infinitely many solutions for a Dirichlet problem involving the p-Laplacian, Proc. roy. Soc. Edinburgh sect. A 140, 737-752 (2010) · Zbl 1197.35125 · doi:10.1017/S0308210509000845
[5]Bonanno, G.; Bisci, G. Molica; O’regan, D.: Infinitely many weak solutions for a class of quasilinear elliptic systems, Math. comput. Modelling 52, 152-160 (2010) · Zbl 1201.35102 · doi:10.1016/j.mcm.2010.02.004
[6]Bonanno, G.; Bisci, G. Molica; Rădulescu, V.: Infinitely many solutions for a class of nonlinear eigenvalue problem in Orlicz–Sobolev spaces, C. R. Acad. sci. Paris, ser. I 349, 263-268 (2011) · Zbl 1211.35110 · doi:10.1016/j.crma.2011.02.009
[7]Bonanno, G.; Bisci, G. Molica; Rădulescu, V.: Infinitely many solutions for a class of nonlinear elliptic problems on fractals, C. R. Acad. sci. Paris, ser. I 350, 387-391 (2012)
[8]Bonanno, G.; Tornatore, E.: Infinitely many solutions for a mixed boundary value problem, Ann. polon. Math. 99, 285-293 (2010) · Zbl 1208.34021 · doi:10.4064/ap99-3-5
[9]Candito, P.; Livrea, R.: Infinitely many solutions for a nonlinear Navier boundary value problem involving the p-biharmonic, Stud. univ. Babes-bolyai math. 55, 41-51 (2010)
[10]Chung, N. T.: Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities, Electron. J. Differential equations 30, 1-12 (2011) · Zbl 1220.35036 · doi:http://www.emis.de/journals/EJDE/Volumes/2011/30/abstr.html
[11]Ricceri, B.: Infinitely many solutions of the Neumann problem for elliptic equations involving the p-Laplacian, Bull. lond. Math. soc. 33, 331-340 (2001) · Zbl 1035.35031 · doi:10.1017/S0024609301008001
[12]Graef, J. R.; Heidarkhani, S.; Kong, L.: A critical points approach for the existence of multiple solutions of a Dirichlet quasilinear system, J. math. Anal. appl. 388, 1268-1278 (2012)
[13]Ghergu, M.; Rădulescu, V.: Singular elliptic problems. Bifurcation and asymptotic analysis, Oxford lecture series in mathematics and its applications 37 (2008)
[14]Kristály, A.; Rădulescu, V.; Varga, C.: Variational principles in mathematical physics, geometry, and economics: qualitative analysis of nonlinear equations and unilateral problems, Encyclopedia of mathematics and its applications 136 (2010)
[15]Ricceri, B.: Nonlinear eigenvalue problems, Handbook of nonconvex analysis and applications, 543-595 (2010) · Zbl 1222.35137
[16]E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. II/B, Berlin, Heidelberg, New York, 1990.
[17]Ricceri, B.: A general variational principle and some of its applications, J. comput. Appl. math. 113, 401-410 (2000) · Zbl 0946.49001 · doi:10.1016/S0377-0427(99)00269-1
[18]Talenti, G.: Some inequalities of Sobolev type on two-dimensional spheres, Internat. ser. Numer. math. 80, 401-408 (1987) · Zbl 0652.26020