Hostname: page-component-7b9c58cd5d-bslzr Total loading time: 0.001 Render date: 2025-03-23T04:41:15.861Z Has data issue: false hasContentIssue false
  • English
  • Français

Aronszajn's theorem for some nonlinear Dirichlet problems with unbounded nonlinearities

Published online by Cambridge University Press:  20 January 2009

Juan J. Nieto
Juan J. Nieto
Affiliation:
Departamento De Analisis MatematicoUniversidad De Santiago, Spain
Rights & Permissions [Opens in a new window]

Extract

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.

We consider the Dirichlet problem

where g is continuous and h ∈ L2(0, π).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 345 - 351
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Ahmad, S., A resonance problem in which the nonlinearity may grow linearly, Proc. Amer. Math. Soc. 82 (1984), 381–384.Google Scholar
2.Aronszajn, A., Le correspondant topologique de l'unicité dans le theorié des équations différentielles, Ann. Math. 43 (1942), 730–738.Google Scholar
3.Ballotti, M. E., Aronszajn's theorem for a parabolic partial differential equation, Nonlinear Anal. 9 (1985), 1183–1187.Google Scholar
4.Cesari, L., Functional analysis, nonlinear differential equations and the alternative method, Nonlinear Functional Analysis and Differential Equations (Cesari, L., Kannan, R. and Schur, J., Eds) (Marcel-Dekker, 1976), 1–197.Google Scholar
5.De Blasi, F. S. and Myjak, J., On the structure of the set of solutions of the Darboux problem for hyperbolic equations, Proc. Edinburgh Math. Soc. 29 (1986), 7–14.Google Scholar
6.GÓrniewicz, L. and Pruszko, T., On the set of solutions of the Darboux problem for some hyperbolic problems, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 38 (1980), 279–285.Google Scholar
7.Hale, J. K., Applications of Alternative Problems (Lecture Notes of Brown University, Providence, R.I., 1971).Google Scholar
8.Hyman, D. M., On decreasing sequences of compact absolute retracts, Fund. Math. 64 (1969), 91–97.Google Scholar
9.Kannan, R., Laksmikantham, V. and Nieto, J. J., Sufficient conditions for existence of solutions of nonlinear boundary value problems at resonance, Nonlinear Anal. 7 (1983), 1013–1020.Google Scholar
10.Kannan, R., Nieto, J. J. and Ray, M. B., A class of nonlinear boundary value problems without Landesman-Lazer condition, J. Math. Anal. Appl. 105 (1985), 1–11.Google Scholar
11.Landesman, E. M. and Lazer, A. C., Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609–623.Google Scholar
12.Pugh, C. C., Funnel sections, J. Differential Equations 19 (1975), 270–295.Google Scholar
13.Rogerts, J. T., The shape of the cross-section of the solution funnel of an ordinary differential equation, Illinois J. Math. 21 (1977), 420–426.Google Scholar