A note on solutions of semilinear equations at resonance in a cone

Bogdan Przeradzki

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 1, page 95-103
  • ISSN: 0066-2216

Abstract

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A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).

How to cite

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Bogdan Przeradzki. "A note on solutions of semilinear equations at resonance in a cone." Annales Polonici Mathematici 58.1 (1993): 95-103. <http://eudml.org/doc/262239>.

@article{BogdanPrzeradzki1993,
abstract = {A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).},
author = {Bogdan Przeradzki},
journal = {Annales Polonici Mathematici},
keywords = {nonnegative solutions; equations at resonance; semilinear problem; resonance; Landesman-Lazer type condition},
language = {eng},
number = {1},
pages = {95-103},
title = {A note on solutions of semilinear equations at resonance in a cone},
url = {http://eudml.org/doc/262239},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Bogdan Przeradzki
TI - A note on solutions of semilinear equations at resonance in a cone
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 1
SP - 95
EP - 103
AB - A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).
LA - eng
KW - nonnegative solutions; equations at resonance; semilinear problem; resonance; Landesman-Lazer type condition
UR - http://eudml.org/doc/262239
ER -

References

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  1. [1] R. E. Gaines and J. Santanilla, A coincidence theorem in convex sets with applications to periodic solutions of ordinary differential equations, Rocky Mountain J. Math. 12 (1982), 669-678. Zbl0508.34030
  2. [2] E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623. Zbl0193.39203
  3. [3] J. L. Mawhin, Topological degree methods in nonlinear boundary value problems, CBMS Regional Conf. Ser. in Math. 40, Amer. Math. Soc., Providence, R.I., 1979. 
  4. [4] B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43. Zbl0746.47043
  5. [5] B. Przeradzki, Operator equations at resonance with unbounded nonlinearities, preprint. 
  6. [6] B. Przeradzki, A new continuation method for the study of nonlinear equations at resonance, J. Math. Anal. Appl., to appear. 
  7. [7] J. Santanilla, Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations, ibid. 126 (1987), 397-408. Zbl0629.34017
  8. [8] J. Santanilla, Existence of nonnegative solutions of a semilinear equation at resonance with linear growth, Proc. Amer. Math. Soc. 105 (1989), 963-971. Zbl0687.47045
  9. [9] S. A. Williams, A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580-586. Zbl0209.13003

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