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On the existence of multiple solutions for a class of nonlinear boundary value problems. (English) Zbl 0273.35037

MSC:
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35J15 Second-order elliptic equations
35J60 Nonlinear elliptic equations
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References:
[1] A. Ambrosetti , Teoria di Lusternik-Schnirelman su varietĂ  con bordo negli spazi di Hilbert , Rend. Sem. Mat. Univ. Padova , 45 ( 1971 ), 337 - 353 . Numdam | MR 388446 | Zbl 0226.58003 · Zbl 0226.58003 · numdam:RSMUP_1971__45__337_0 · eudml:107384
[2] F.E. Browder , Infinite dimensional manifolds and nonlinear elliptic eigenvalue problems , Ann. Math. , 82 ( 1965 ), 459 - 477 . MR 203249 | Zbl 0136.12002 · Zbl 0136.12002 · doi:10.2307/1970708
[3] J.A. Hempel , Multiple solutions for a class of nonlinear boundary value problems , Ind. Univ. Math. J. , 20 ( 1971 ), 983 - 996 . MR 279423 | Zbl 0225.35045 · Zbl 0225.35045 · doi:10.1512/iumj.1971.20.20094
[4] R.S. Palais , Lusternik-Schnirelman theory on Banach manifolds , Topology , 5 ( 1966 ), 115 - 132 . MR 259955 | Zbl 0143.35203 · Zbl 0143.35203 · doi:10.1016/0040-9383(66)90013-9
[5] J.T. Schwartz , Generalizing the Lusternik-Schnirelman theory of critical points , Comm. Pure Appl. Math. , 17 ( 1964 ), 307 - 315 . MR 166796 | Zbl 0152.40801 · Zbl 0152.40801 · doi:10.1002/cpa.3160170304
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