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Semilinear elliptic problems near resonance with a nonprincipal eigenvalue. (English) Zbl 1149.35044
Summary: We consider the Dirichlet problem for the equation -Δu=λu±f(x,u)+h(x) in a bounded domain, where f has a sublinear growth and hL 2 . We find suitable conditions on f and h in order to have at least two solutions for λ near to an eigenvalue of -Δ. A typical example to which our results apply is when f(x,u) behaves at infinity like a(x)|u| q-2 u, with M>a(x)>δ>0, and 1<q<2.
35J65Nonlinear boundary value problems for linear elliptic equations
35P05General topics in linear spectral theory of PDE
58J50Spectral problems; spectral geometry; scattering theory
[1]Mawhin, J.; Schmitt, K.: Nonlinear eigenvalue problems with the parameter near resonance, Ann. polon. Math. 51, 241-248 (1990) · Zbl 0724.34025
[2]Badiale, M.; Lupo, D.: Some remarks on a multiplicity result by mawhin and schmitt, Acad. roy. Belg. bull. Cl. sci. (5) 65, No. 6 – 9, 210-224 (1989) · Zbl 0706.34020
[3]Lupo, D.; Ramos, M.: Some multiplicity results for two-point boundary value problems near resonance, Rend. sem. Mat. univ. Politec. Torino 48, No. 2, 125-135 (1990) · Zbl 0764.34017
[4]Chiappinelli, R.; Mawhin, J.; Nugari, R.: Bifurcation from infinity and multiple solutions for some Dirichlet problems with unbounded nonlinearities, Nonlinear anal. 18, No. 12, 1099-1112 (1992) · Zbl 0780.35038 · doi:10.1016/0362-546X(92)90155-8
[5]Chiappinelli, R.; De Figueiredo, D. G.: Bifurcation from infinity and multiple solutions for an elliptic system, Differential integral equations 6, No. 4, 757-771 (1993) · Zbl 0784.35008
[6]Ma, T. F.; Ramos, M.; Sanchez, L.: Multiple solutions for a class of nonlinear boundary value problems near resonance: A variational approach, , 3301-3311 (1997) · Zbl 0887.35053 · doi:10.1016/S0362-546X(96)00380-X
[7]Ramos, M.; Sanchez, L.: A variational approach to multiplicity in elliptic problems near resonance, Proc. roy. Soc. Edinburgh sect. A 127, No. 2, 385-394 (1997) · Zbl 0869.35041 · doi:10.1017/S0308210500023696
[8]Ma, T. F.; Pelicer, M. L.: Perturbations near resonance for the p-Laplacian in RN, Abstr. appl. Anal. 7, No. 6, 323-334 (2002) · Zbl 1065.35116 · doi:10.1155/S1085337502203073
[9]De Nápoli, P.; Mariani, M.: Three solutions for quasilinear equations in rn near resonance, Electron. J. Differ. equ. Conf. 6, 131-140 (2001) · Zbl 1014.35027 · doi:emis:journals/EJDE/conf-proc/06/d1/abstr.html
[10]Moroz, V.: On the Morse critical groups for indefinite sublinear elliptic problems, Nonlinear anal. 52, No. 5, 1441-1453 (2003) · Zbl 1087.35040 · doi:10.1016/S0362-546X(02)00174-8
[11]Moroz, V.: Solutions of superlinear at zero elliptic equations via Morse theory, Topol. methods nonlinear anal. 10, No. 2, 387-397 (1997) · Zbl 0919.35048
[12]Wu, S.; Yang, H.: A class of resonant elliptic problems with sublinear nonlinearity at origin and at infinity, Nonlinear anal. 45, No. 7, 925-935 (2001) · Zbl 1107.35348 · doi:10.1016/S0362-546X(99)00425-3
[13]Marino, A.; Micheletti, A. M.; Pistoia, A.: A nonsymmetric asymptotically linear elliptic problem, Topol. methods nonlinear anal. 4, No. 2, 289-339 (1994) · Zbl 0844.35035
[14]Frigon, M.: On a new notion of linking and application to elliptic problems at resonance, J. differential equations 153, No. 1, 96-120 (1999) · Zbl 0922.35044 · doi:10.1006/jdeq.1998.3540
[15]De Figueiredo, D. G.: Lectures on the Ekeland variational principle with applications and detours, Tata inst. Fund. res. Lect. math. Phys. 81 (1989)
[16]Rabinowitz, P. H.: Minimax methods in critical point theory with applications to differential equations, CBMS reg. Conf. ser. Math. 65 (1986) · Zbl 0609.58002
[17]Chang, K.: Infinite-dimensional Morse theory and multiple solution problems, Progr. nonlinear differential equations appl. 6 (1993) · Zbl 0779.58005
[18]Su, J.; Tang, C.: Multiplicity results for semilinear elliptic equations with resonance at higher eigenvalues, Nonlinear anal. 44, No. 3, 311-321 (2001) · Zbl 1153.35336 · doi:10.1016/S0362-546X(99)00265-5