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Landesman-Lazer-alternative theorems for a class of nonlinear functional equations. (English) Zbl 0372.47032


MSC:

47J05 Equations involving nonlinear operators (general)
47F05 General theory of partial differential operators
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References:

[1] Frehse, J.: An existence theorem for a class of non-coercive optimization and variational problems. Math. Z.159, 51-63 (1978) · Zbl 0386.49006 · doi:10.1007/BF01174568
[2] Frehse, J.: Solvability and alternative theorems for a class of non-linear functional equations in Banach spaces. Arkiv för Matematik · Zbl 0427.47047
[3] Frehse, J.: Existence and alternative theorems for semi-coercive problems and applications to non-linear elliptic equations. SFB-Preprint 175. Universität Bonn
[4] Frehse, J.: A Landesman-Lazer alternative theorem for a class of optimization problems · Zbl 0431.49003
[5] Fucik, S.: Ranges of non-linear operators, Vols. I?V. Dept. of Mathematics Charles University Praha · Zbl 0332.47032
[6] Hess, P.: On a class of strongly non-linear elliptic variational inequalities. Math. Ann.211, 289-297 (1974) · Zbl 0285.49003 · doi:10.1007/BF01418226
[7] Hess, P.: On semi-coercive non-linear problems. Indiana Univ. Math. J.23, 645-654 (1974) · Zbl 0269.47029 · doi:10.1512/iumj.1974.23.23055
[8] Hess, P.: Non-linear perturbations of linear elliptic and parabolic problems at resonance: existence of multiple solutions. To appear in Ann. Sc. Norm. Sup. Pisa · Zbl 0392.35051
[9] Gaines, R. E., and Mawhin, J. L.: Coincidence degree and non-linear differential equations, pp. 134-165, Lecture Notes in Mathematics 568. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0339.47031
[10] Landesman, E. M., and Lazar, A. C.: Non-linear perturbations of linear elliptic boundary value problems at resonance. J. Math. Mech.19, 609-623 (1970) · Zbl 0193.39203
[11] Mawhin, J.: Landesman-Lazer’s type problems for non-linear equations. Conference del Seminario di Matematica dell’ Università di Bari. No. 147 (1977) · Zbl 0436.47050
[12] Morrey, C. B., Jr.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0142.38701
[13] Ne?as, J.: On the range of non-linear operators with linear asymptotes which are not invertible. Comment. Math. Univ. Carolinae14, 63-72 (1973) · Zbl 0257.47032
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