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Multiple positive solutions of superlinear elliptic problems with sign-changing weight. (English) Zbl 1210.35089
Summary: We study the existence of multiple positive solutions for a superlinear elliptic PDE with a sign-changing weight. Our approach is variational and relies on classical critical point theory on smooth manifolds. A special care is paid to the localization of minimax critical points.

MSC:
35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
47J30 Variational methods involving nonlinear operators
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[1] Alama, S.; Tarantello, G., Elliptic problems with nonlinearities indefinite in sign, J. funct. anal., 141, 159-215, (1996) · Zbl 0860.35032
[2] Amann, H.; Ambrosetti, A.; Mancini, G., Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities, Math. Z., 158, 179-194, (1978) · Zbl 0368.35032
[3] Amann, H.; López-Gómez, J., A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. differential equations, 146, 336-374, (1998) · Zbl 0909.35044
[4] Berestycki, H.; Dolcetta, I.C.; Nirenberg, L., Variational methods for indefinite superlinear homogeneous elliptic problems, Nodea, 2, 553-572, (1995) · Zbl 0840.35035
[5] Butler, G.J., Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear differential equations, J. differential equations, 22, 467-477, (1976) · Zbl 0299.34050
[6] Gaudenzi, M.; Habets, P.; Zanolin, F., Positive solutions of superlinear boundary value problems with singular indefinite weight, Comm. pure appl. anal., 2, 411-423, (2003) · Zbl 1048.34046
[7] Gaudenzi, M.; Habets, P.; Zanolin, F., A seven positive solutions theorem for a superlinear problems, Adv. nonlinear stud., 4, 121-136, (2004)
[8] Gilbarg, D.; Trudinger, N.S., Elliptic partial differential equations of second order, () · Zbl 0691.35001
[9] Kavian, O., Introduction à la théorie des points critiques et applications aux problèmes elliptiques, () · Zbl 0797.58005
[10] López-Gómez, J., Varying bifurcation diagrams of positive solutions for a class of indefinite superlinear boundary value problems, Trans. amer. math. soc., 352, 1825-1858, (2000) · Zbl 0940.35095
[11] Papini, D.; Zanolin, F., A topological approach to superlinear indefinite boundary value problems, Topological methods nonlinear anal., 15, 203-233, (2000) · Zbl 0990.34019
[12] Rabinowitz, P.H., Minimax methods in critical point theory with applications to differential equations, Cbms, 65, (1986) · Zbl 0609.58002
[13] Terracini, S.; Verzini, G., Oscillating solutions to second order ODE’s with indefinite superlinear nonlinearities, Nonlinearity, 13, 1501-1514, (2000) · Zbl 0979.34028
[14] Willem, M., Minimax theorems, () · Zbl 0856.49001
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