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Nontrivial solutions of equations with potential operators. (English. Russian original) Zbl 0487.47040
Sib. Math. J. 21, 773-786 (1981); translation from Sib. Mat. Zh. 21, 28-45 (1980).

47J05 Equations involving nonlinear operators (general)
47H05 Monotone operators and generalizations
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Full Text: DOI
[1] D. C. Clark, ?A variant of the Liusternik-Schnirelman theorem,? Indiana Univ. Math. J.,22, 65-74 (1972). · Zbl 0228.58006 · doi:10.1512/iumj.1972.22.22008
[2] A. Ambrosetti and P. H. Rabinowitz, ?Dual variational methods in critical point theory and applications,? J. Func. Anal.,14, 349-381 (1973). · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[3] R. S. Palais, ?Liusternik-Schnirelman theory on Banach manifolds,? Topology,5, 115-132 (1966). · Zbl 0143.35203 · doi:10.1016/0040-9383(66)90013-9
[4] J. P. Goossez, ?Nonlinear elliptic boundary value problems for equations with rapidly or slowly increasing coefficients,? Trans. Am. Math. Soc.,190, 163-205 (1974). · doi:10.1090/S0002-9947-1974-0342854-2
[5] J. L. Lions, Non-Homogeneous Boundary Value Problems, Springer-Verlag (1972).
[6] M. M. Vainberg, Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, Halsted Press (1974). · Zbl 0293.35026
[7] L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977). · Zbl 0127.06102
[8] M. A. Krasnosel’skii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Fizmatgiz, Moscow (1958).
[9] S. L. Sobolev, Introduction to the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1974).
[10] Yu. G. Reshetnyak, ?General theorems on the semicontinuity and convergence with a functional,? Sib. Mat. Zh.,8, No. 5, 1051-1069 (1967).
[11] I. V. Skrypnik, Nonlinear Elliptic Equations of Higher Order [in Russian], Naukova Dumka, Kiev (1973). · Zbl 0296.35032
[12] S. I. Al’ber, ?The topology of functional manifolds and global variational calculus,? Usp. Mat. Nauk,25, No. 4, 57-122 (1970).
[13] V. S. Klimov, ?On the rotation of potential vector fields,? Mat. Zametki,20, No. 2, 258-260 (1976). · Zbl 0344.46094
[14] M. A. Krasnosel’skii, Topological Methods in the Theory of Nonlinear Integral Equations [in Russian], Gostekhizdat, Moscow (1956).
[15] C. V. Coffman, ?A minimum?maximum principle for a class of nonlinear equations,? J. d’Anal. Math.,22, 391-419 (1969). · Zbl 0179.15601 · doi:10.1007/BF02786802
[16] A. S. Shvarts, ?Some estimates of the genus of a topological space in the sense of Krasnosel’skii,? Usp. Mat. Nauk,12, No. 4, 209-214 (1957).
[17] V. S. Klimov, ?On functionals with an infinite number of critical values,? Mat. Sb.,100, No. 1, 101-115 (1976).
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