Boundary value problems via an intermediate value theorem
Abstract:
We use an intermediate value theorem for quasimonotone increasing
functions to prove the existence of a smallest and a greatest solution of the
Dirichlet problem $u'' + f(t,u) = 0, u(0) = \alpha, u(1) = \beta$ between
lower and upper solutions, where $f: [0,1] \times E \to E$ is quasimonotone
increasing in its second variable with respect to a regular cone.
functions to prove the existence of a smallest and a greatest solution of the
Dirichlet problem $u'' + f(t,u) = 0, u(0) = \alpha, u(1) = \beta$ between
lower and upper solutions, where $f: [0,1] \times E \to E$ is quasimonotone
increasing in its second variable with respect to a regular cone.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2007 |
| Sprache | Englisch |
| Identifikator | KITopen-ID: 1000006912 |
| Verlag | Universität Karlsruhe (TH) |
| Serie | Preprint. Fakultät für Mathematik, Universität Karlsruhe ; 2007,12 |