Existence theorems across a point of resonance

Author:
Lamberto Cesari

Journal:
Bull. Amer. Math. Soc. **82** (1976), 903-906

MSC (1970):
Primary 47H15, 34B15, 34C15, 35G30, 35J40

MathSciNet review:
0425693

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References | Similar Articles | Additional Information

**1.**Lamberto Cesari,*Functional analysis and periodic solutions of nonlinear differential equations*, Contributions to Differential Equations**1**(1963), 149–187. MR**0151678****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. MR**0430884****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. MR**0467420****4.**Lamberto Cesari,*Nonlinear oscillations across a point of resonance for nonselfadjoint systems*, J. Differential Equations**28**(1978), no. 1, 43–59. MR**0477909****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. MR**499091****6.**L. Cesari and R. Kannan,*An abstract existence theorem at resonance*, Proc. Amer. Math. Soc.**63**(1977), no. 2, 221–225. MR**0448180**, 10.1090/S0002-9939-1977-0448180-3**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. MR**0437924****8.**R. Kannan and P. J. McKenna,*An existence theorem by alternative methods for semilinear abstract equations*, Boll. Un. Mat. Ital. (to appear).**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. MR**0267269****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. MR**0249731****11.**Jindřich Nečas,*The range of nonlinear operators with linear asymptotes which are not invertible*, Comment. Math. Univ. Carolinae**14**(1973), 63–72. MR**0318995****12.**H. C. Shaw,*Nonlinear elliptic boundary value problems at resonance*, J. Differential Equations (to appear).**13.**S. A. Williams,*A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem*, J. Differential Equations**8**(1970), 580–586. MR**0267267**

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DOI:
http://dx.doi.org/10.1090/S0002-9904-1976-14205-X