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References
R. Adams, Sobolev Spaces, Academic Press, New York, San Francisco, London (1975).
S. Ahmad, A.C. Lazer and J. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933–944.
H. Amann, Saddle points and multiple solutions of differential equations, Math. Z. (1979), 127–166.
A. Ambrosetti, and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Annali Math. Pura Appl., 93 (1972) 231–247.
P. Bates and A. Castro, Existence and uniqueness for a variational hyperoblic system without resonance, Nonlinear Analysis, Theory, Methods and Applications, 4 (1980), 1151–1156.
P. Bates and A. Castro, Necessary and sufficient conditions fon existence of solutions to equations with noninvertible linear part, to appear in volume XV (numbers 1–2) of the Revista Colombiana de Matemáticas.
A. Castro, Hammerstein integral equations with indefinite Kernel, Internat. J. Math. and Math. Sci., 1 (1978), 187–201.
A. Castro, A two point boundary value problem with jumping nonlinearities, Proc. Amer. Math. Soc., 79 (1980), 207–211.
A. Castro, Periodic solutions of the forced pendulum equation, Differential Equations, Editors S. Ahmad, M. Keener and A.C. Lazer, Academic Press (1980), 149–160.
A. Castro, Existence of infinitely many solutions for a class of superlinear problems, (preprint).
A. Castro, Métodos variacionales y análisis functional no lineal, edited by the Universidad Pedagógica y Tecnológ ca de Colombia and the Sociedad Colombiana de Matemáticas (1980).
A. Castro and A. C. Lazer, Applications of a maxmin principle, Rev. Colombiana Mat., 10 (1976), 141–149.
A. Castro and A. C. Lazer, Critical point theory and the number of solutions of a nonlinear Dirichlet problem. Annali Mat. Pura Appl., CXX (1979), 113–137.
E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic equations at resonance, J. Math. Mech., 19 (1970), 609–623.
A. C. Lazer, E. M. Landesman and D. Meyers, On saddle point problems in the calculus of variations, the Ritz algorithm, and monotone convergence, J. Math. Anal. Appl., 52 (1975), 594–614.
L. A. Lusternik and V. J. Sobolev, Functional analysis, Hindustan Publishing Corpn. (India), Delhi (1961).
L. Nirenberg, Variational and topological methods in nonlinear problems, Bull. A. Math. Soc., 4 (1981), 267–302.
P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), 157–184.
H. L. Royden, Real analysis, McMillan Publishing Co., New York (1968).
M. Vainberg, Variational methods for the study of nonlinear operators, Holden Day, San Francisco (1964).
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Alfonso, C.B. (1982). Reduction methods via minimax. In: Guedes de Figueiredo, D., Hönig, C.S. (eds) Differential Equations. Lecture Notes in Mathematics, vol 957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066231
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DOI: https://doi.org/10.1007/BFb0066231
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