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Three weak solutions for elliptic Dirichlet problems. (English) Zbl 1225.35067
An existence result of three non-zero solutions for non-autonomous elliptic Dirichlet problems, under suitable assumptions on the nonlinear term, is presented. The approach is based on a recent three critical points theorem for differentiable functionals.
MSC:
35J15Second order elliptic equations, general
35J20Second order elliptic equations, variational methods
35J50Systems of elliptic equations, variational methods
References:
[1]Agmon, S.: The lp approach to the Dirichlet problem, Ann. sc. Norm. super. Pisa 13, 405-448 (1959) · Zbl 0093.10601 · doi:numdam:ASNSP_1959_3_13_4_405_0
[2]Ambrosetti, A.; Rabinowitz, P. H.: Dual variational methods in critical point theory and applications, J. funct. Anal. 14, 349-381 (1973) · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[3]Bonanno, G.; Candito, P.: Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. differential equations 244, 3031-3059 (2008) · Zbl 1149.49007 · doi:10.1016/j.jde.2008.02.025
[4]Bonanno, G.; Marano, S. A.: On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. anal. 89, 1-10 (2010) · Zbl 1194.58008 · doi:10.1080/00036810903397438
[5]Castro, A.; Cossio, J.: Multiple solutions for a nonlinear Dirichlet problem, SIAM J. Math. anal. 25, 1554-1561 (1994) · Zbl 0807.35039 · doi:10.1137/S0036141092230106
[6]Cossio, J.; Herrón, S.; Vélez, C.: Existence of solutions for an asymptotically linear Dirichlet problem via lazer-solimini results, Nonlinear anal. 71, 66-71 (2009) · Zbl 1168.35364 · doi:10.1016/j.na.2008.10.031
[7]Gilbarg, D.; Trudinger, N. S.: Elliptic partial differential equations of second order, (1983)
[8]Kristály, A.; Rădulescu, V.; Varga, Cs.: Variational principles in mathematical physics, geometry, and economics: qualitative analysis of nonlinear equations and unilateral problems, Encyclopedia math. Appl. 136 (2010)
[9]Landesman, E. M.; Lazer, A. C.: Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. math. Mech. 19, 609-623 (1970) · Zbl 0193.39203
[10]Micheletti, A. M.; Pistoia, A.: A variational viewpoint of the existence of three solutions for some nonlinear elliptic problem, Differential integral equations 9, 1029-1042 (1996) · Zbl 0851.35042
[11]Rabinowitz, P. H.: Minimax methods in critical point theory with applications to differential equations, CBMS reg. Conf. ser. Math. 65 (1986) · Zbl 0609.58002
[12]Ricceri, B.: On a three critical points theorem, Arch. math. (Basel) 75, 220-226 (2000) · Zbl 0979.35040 · doi:10.1007/s000130050496
[13]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
[14]Ricceri, B.: Existence of three solutions for a class of elliptic eigenvalue problems, Math. comput. Modelling 32, 1485-1494 (2000) · Zbl 0970.35089 · doi:10.1016/S0895-7177(00)00220-X
[15]Talenti, G.: Best constants in Sobolev inequality, Ann. mat. Pura appl. 110, 353-372 (1976) · Zbl 0353.46018 · doi:10.1007/BF02418013