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Existence theorems across a point of resonance. (English) Zbl 0341.47040


MSC:

47J05 Equations involving nonlinear operators (general)
34B15 Nonlinear boundary value problems for ordinary differential equations
35G30 Boundary value problems for nonlinear higher-order PDEs
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
35J40 Boundary value problems for higher-order elliptic equations
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[1] Lamberto Cesari, Functional analysis and periodic solutions of nonlinear differential equations, Contributions to Differential Equations 1 (1963), 149 – 187. · Zbl 0075.25601
[2] Lamberto Cesari, Alternative methods in nonlinear analysis, International Conference on Differential Equations (Proc., Univ. Southern California, Los Angeles, Calif., 1974) Academic Press, New York, 1975, pp. 95 – 148. · Zbl 0309.35016
[3] Lamberto Cesari, An abstract existence theorem across a point of resonance, Dynamical systems (Proc. Internat. Sympos., Univ. Florida, Gainesville, Fla., 1976) Academic Press, New York, 1977, pp. 11 – 26. · Zbl 0341.47040
[4] Lamberto Cesari, Nonlinear oscillations across a point of resonance for nonselfadjoint systems, J. Differential Equations 28 (1978), no. 1, 43 – 59. · Zbl 0395.34034 · doi:10.1016/0022-0396(78)90079-7
[5] Lamberto Cesari, Nonlinear problems across a point of resonance for nonselfadjoint systems, Nonlinear analysis (collection of papers in honor of Erich H. Rothe), Academic Press, New York, 1978, pp. 43 – 67. · Zbl 0395.34034
[6] L. Cesari and R. Kannan, An abstract existence theorem at resonance, Proc. Amer. Math. Soc. 63 (1977), no. 2, 221 – 225. · Zbl 0361.47021
[7] Djairo Guedes de Figueiredo, The Dirichlet problem for nonlinear elliptic equations: a Hilbert space approach, Partial differential equations and related topics (Program, Tulane Univ., New Orlenas, La., 1974) Springer, Berlin, 1975, pp. 144 – 165. Lecture Notes in Math., Vol. 446. · Zbl 0296.35038
[8] R. Kannan and P. J. McKenna, An existence theorem by alternative methods for semilinear abstract equations, Boll. Un. Mat. Ital. (to appear). · Zbl 0352.47030
[9] E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1969/1970), 609 – 623. · Zbl 0193.39203
[10] A. C. Lazer and D. E. Leach, Bounded perturbations of forced harmonic oscillators at resonance, Ann. Mat. Pura Appl. (4) 82 (1969), 49 – 68. · Zbl 0194.12003 · doi:10.1007/BF02410787
[11] Jindřich Nečas, The range of nonlinear operators with linear asymptotes which are not invertible, Comment. Math. Univ. Carolinae 14 (1973), 63 – 72.
[12] H. C. Shaw, Nonlinear elliptic boundary value problems at resonance, J. Differential Equations (to appear). · Zbl 0341.35039
[13] S. A. Williams, A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580 – 586. · Zbl 0209.13003 · doi:10.1016/0022-0396(70)90031-8
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