Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T10:36:42.605Z Has data issue: false hasContentIssue false
  • English
  • Français

AN EXISTENCE RESULT OF ONE NONTRIVIAL SOLUTION FOR TWO POINT BOUNDARY VALUE PROBLEMS

Part of: Boundary value problems

Published online by Cambridge University Press:  13 July 2011

GABRIELE BONANNO  and
ANGELA SCIAMMETTA
GABRIELE BONANNO*
Affiliation:
Department of Science for Engineering and Architecture (Mathematics Section), Engineering Faculty, University of Messina, 98166 Messina, Italy (email: [email protected])
ANGELA SCIAMMETTA
Affiliation:
Department of Mathematics, University of Messina, 98166 Messina, Italy (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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.

Existence results of positive solutions for a two point boundary value problem are established. No asymptotic condition on the nonlinear term either at zero or at infinity is required. A classical result of Erbe and Wang is improved. The approach is based on variational methods.

Keywords

boundary value problempositive solutions

MSC classification

Secondary: 34B15: Nonlinear boundary value problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 288 - 299
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Agarwal, P. R., O’Regan, D. and Wong, P. J. Y., Positive Solutions of Differential, Difference and Integral Equations (Kluwer, Dordrecht, 1999).CrossRefGoogle Scholar
[2]Averna, D. and Bonanno, G., ‘A three critical points theorem and its applications to the ordinary Dirichlet problem’, Topol. Methods Nonlinear Anal. 22 (2003), 93–103.CrossRefGoogle Scholar
[3]Bereanu, C. and Mawhin, J., ‘Boundary value problems for some nonlinear systems with singular Φ-laplacian’, J. Fixed Point Theory Appl. 4 (2008), 57–75.CrossRefGoogle Scholar
[4]Bonanno, G., ‘A critical point theorem via the Ekeland variational principle’, Preprint.Google Scholar
[5]Bonanno, G. and Candito, P., ‘Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities’, J. Differential Equations 244 (2008), 3031–3059.CrossRefGoogle Scholar
[6]Capietto, A. and Dambrosio, W., ‘Boundary value problems with sublinear conditions near zero’, NoDEA: Nonlinear Differential Equations Appl. 6 (1999), 149–172.Google Scholar
[7]Capietto, A., Mawhin, J. and Zanolin, F., ‘Boundary value problems for forced superlinear second order ordinary differential equations’, in: Nonlinear Partial Differential Equations, Collège de France Seminar (Longman, New York, 1994), pp. 55–94.Google Scholar
[8]Cîrstea, F., Ghergu, M. and Rădulescu, V., ‘Combined effects of asymptotically linear and singular nonlinearities in bifurcation problems of Lane–Emden–Fowler type’, J. Math. Pures Appl. 84 (2005), 493–508.CrossRefGoogle Scholar
[9]Erbe, L. H. and Wang, H., ‘On the existence of positive solutions of ordinary differential equations’, Proc. Amer. Math. Soc. 120 (1994), 743–748.Google Scholar
[10]Ghergu, M. and Rădulescu, V., ‘On a class of sublinear singular elliptic problems with convection term’, J. Math. Anal. Appl. 311 (2005), 635–646.CrossRefGoogle Scholar
[11]Hirano, N., ‘Existence of infinitely many solutions for sublinear elliptic problems’, J. Math. Anal. Appl. 278 (2003), 83–92.CrossRefGoogle Scholar
[12]Naito, Y. and Tanaka, S., ‘On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations’, Nonlinear Anal. 56 (2004), 919–935.CrossRefGoogle Scholar
[13]Ricceri, B., ‘A general variational principle and some of its applications’, J. Comput. Appl. Math. 113 (2000), 401–410.Google Scholar
[14]Shi, J. and Yao, M., ‘Positive solutions for elliptic equations with singular nonlinearity’, Electron. J. Differential Equations 4 (2005), 1–11.Google Scholar
[15]Struwe, M., Variational Methods (Springer, Berlin, 1996).Google Scholar