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Existence and multiplicity of solutions to 2mth-order ordinary differential equations
- Source :
-
Journal of Mathematical Analysis & Applications . Jul2007, Vol. 331 Issue 2, p958-977. 20p. - Publication Year :
- 2007
-
Abstract
- Abstract: In this paper, the existence and multiplicity of solutions are obtained for the 2mth-order ordinary differential equation two-point boundary value problems for all subject to Dirichlet, Neumann, mixed and periodic boundary value conditions, respectively, where f is continuous, for all . Since these four boundary value problems have some common properties and they can be transformed into the integral equation of form , we firstly deal with this nonlinear integral equation. By using the strongly monotone operator principle and the critical point theory, we establish some conditions on f which are able to guarantee that the integral equation has a unique solution, at least one nonzero solution, and infinitely many solutions. Furthermore, we apply the abstract results on the integral equation to the above four 2mth-order two-point boundary problems and successfully resolve the existence and multiplicity of their solutions. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 331
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 24457892
- Full Text :
- https://doi.org/10.1016/j.jmaa.2006.09.025