Existence of nodal solutions for Lidstone eigenvalue problems
โ Scribed by Jia Xu; XiaoLing Han
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 194 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0362-546X
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๐ SIMILAR VOLUMES
We investigate the existence of nodal solutions of an indefinite weight boundary value problem where h โ C [0, 1] changes sign. The proof of our main result is based upon bifurcation techniques.
Using global bifurcation theory, we obtain the existence of solutions with specified numbers of simple generalized zeros for the nonlinear eigenvalue problem on time scales T where r > 0 is a given constant. In addition, we argue that our existence theorem is a generalization of a previous result w
In this work, we consider the nonlinear eigenvalue problems s exist. Using global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above asymptotically linear eigenvalue problems.
For the 2mth order Lidstone boundary value problem, where -1 m f m โ 0 โ is continuous, growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions. This generalizes earlier papers which have applied Avery's generalization of the Leggett-Williams theo