Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-08T18:48:26.824Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on superlinear boundary value problems

Published online by Cambridge University Press:  17 April 2009

Svatopluk Fučík
Svatopluk Fučík
Affiliation:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Prague, Czechoslovakia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Necessary and sufficient conditions for the weak solvability of the Dirichlet problem for nonlinear differential equations of the second order are proved. The differential operators considered are in the form of a sum of a linear noninvertible operator, with the null-space generated by a positive function, and a monotone nonlinear perturbation, the growth of which is more than linear.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 181 - 188
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Ambrosetti, A., Prodi, G., “On the inversion of some differentiable mappings with singularities between Banach spaces”, Ann. Mat. Pura Appl. 93 (1972), 231–246.CrossRefGoogle Scholar
[2]Browder, Felix E., Problèmes non linéaires (Séminaire de Mathématiques Supérieures, 15 (Été, 1965). Les Presses de l'Université de Montréal, Montreal, Quebec, 1966).Google Scholar
[3]Fučík, Svatopluk, “Surjectivity of operators involving linear noninvertible part and nonlinear compact perturbation”, Funkcial. Ekvac. 17 (1974), 73–83.Google Scholar
[4]Fučík, Svatopluk, “Nonlinear equations with noninvertible linear part”, Czechoslovak Math. J. 24 (99)(1974), 467–495.CrossRefGoogle Scholar
[5]Fučík, Svatopluk, “Remarks on a result by A. Ambrosetti and G. Prodi”, Boll. Un. Mat. Ital. (4) 11 (1975), 259–267.Google Scholar
[6]Fučík, Svatopluk, Krbec, M., “Boundary value problems with bounded nonlinearity and general null-space of the linear part”, submitted.Google Scholar
[7]Fučík, Svatopluk and Kučera, Milan and Nečas, Jindřich, “Ranges of nonlinear assymptotically linear operators”, J. Differential Equations 17 (1975), 375–394.CrossRefGoogle Scholar
[8]Kazdan, Jerry L. and Warner, F.W., “Remarks on some quasilinear elliptic equations”, Comm. Pure Appl. Math. 28 (1975), 567–597.CrossRefGoogle Scholar
[9]Landesman, E.M. & Lazer, A.C., “Nonlinear perturbations of linear elliptic boundary value problems at resonance”, J. Math. Mech. 19 (1969/1970), 609–623.Google Scholar