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Multiple solutions of superlinear elliptic equations. (English) Zbl 1223.35173
Summary: We give some multiplicity results on existence of nontrivial solutions for superlinear elliptic equations with a saddle structure near 0. We make use of a combination of bifurcation theory and minimax methods.

35J65Nonlinear boundary value problems for linear elliptic equations
58E05Abstract critical point theory
Full Text: DOI
[1] A. AMBROSETTI - P. H. RABINOWITZ, Dual variational methods in critical point theory and applications , J. Funct. Anal. 14 (1973), 349-381. · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[2] A. AMBROSETTI - J. GARCÍA AZORERO - I. PERAL, Multiplicity results for some nonlinear elliptic equations , J. Funct. Anal. 137 (1996), 219-242. · Zbl 0852.35045 · doi:10.1006/jfan.1996.0045
[3] T. BARTSCH - K. C. CHANG - Z.-Q. WANG, On the Morse indices of sign changing solutions of nonlinear elliptic problems , Math. Z. 233 (2000), 655-677. · Zbl 0946.35023 · doi:10.1007/s002090050492
[4] T. BARTSCH - Z.-Q. WANG, On the existence of sign changing solutions for semilinear Dirichlet problems , Topol. Methods Nonlinear Anal. 7 (1996), 115-131. · Zbl 0903.58004
[5] A. CASTRO - J. COSSIO - J. NEUBERGER, A sign-changing solution for a superlinear Dirichlet problem , Rocky Mountain J. Math. 27 (1997), 1041-1053. · Zbl 0907.35050 · doi:10.1216/rmjm/1181071858 · http://math.la.asu.edu/~rmmc/rmj/VOL27-4/CONT27-4/CONT27-4.html
[6] K. C. CHANG, Infinite Dimensional Morse Theory and Multiple Solution Problems , Progr. Nonlinear Differential Equations Appl. 6, Birkhäuser, Boston, 1993. · Zbl 0779.58005
[7] E. N. DANCER - Y. H. DU, A note on multiple solutions of some semilinear elliptic problems , J. Math. Anal. Appl. 211 (1997), 626-640. · Zbl 0880.35046 · doi:10.1006/jmaa.1997.5471