PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1993 | 58 | 1 | 95-103
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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]).
Kategorie tematyczne
Rocznik
Tom
58
Numer
1
Strony
95-103
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-06-17
Twórcy
  • Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [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.
  • [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.
  • [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] B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43.
  • [5] B. Przeradzki, Operator equations at resonance with unbounded nonlinearities, preprint.
  • [6] B. Przeradzki, A new continuation method for the study of nonlinear equations at resonance, J. Math. Anal. Appl., to appear.
  • [7] J. Santanilla, Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations, ibid. 126 (1987), 397-408.
  • [8] J. Santanilla, Existence of nonnegative solutions of a semilinear equation at resonance with linear growth, Proc. Amer. Math. Soc. 105 (1989), 963-971.
  • [9] S. A. Williams, A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580-586.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv58z1p95bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.