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Global Structure of Positive Solutions of Fourth-Order Problems with Clamped Beam Boundary Conditions
- Source :
- Mathematical Notes. 109:962-970
- Publication Year :
- 2021
- Publisher :
- Pleiades Publishing Ltd, 2021.
-
Abstract
- In this paper, we investigate the global structure of positive solutions of $$\begin{cases} u''''(x)=\lambda h(x)f(u(x)), & 0 0$$ is a parameter, $$h\in C[0,1]$$ , $$f\in C[0,\infty)$$ and $$f(s)>0$$ for $$s>0$$ . We show that the problem has three positive solutions suggesting suitable conditions on the nonlinearity. Furthermore, we also establish the existence of infinitely many positive solutions. The proof is based on the bifurcation method.
Details
- ISSN :
- 15738876 and 00014346
- Volume :
- 109
- Database :
- OpenAIRE
- Journal :
- Mathematical Notes
- Accession number :
- edsair.doi...........f8a382109ec9a16fb599540257ba651f