MULTIPLE POSITIVE SOLUTIONS OF RESONANT AND NON-RESONANT NON-LOCAL FOURTH-ORDER BOUNDARY VALUE PROBLEMS

We study the existence of positive solutions for equations of the form \begin{linenomath}$$u^{(4)}(t)-{\omega}^4 u(t)=f(t, u(t)),\;\;\text{a.e.} \;\; t \in (0,1),$$\end{linenomath} where 0 < ω < π, subject to various non-local boundary conditions defined in terms of the Riemann–Stieltjes integ...

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Bibliographic Details
Published in:Glasgow mathematical journal 2012-01, Vol.54 (1), p.225-240
Main Authors: WEBB, J. R. L., ZIMA, M.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Equivalence
Integrals
Mathematical analysis
Mathematics
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Summary:We study the existence of positive solutions for equations of the form \begin{linenomath}$$u^{(4)}(t)-{\omega}^4 u(t)=f(t, u(t)),\;\;\text{a.e.} \;\; t \in (0,1),$$\end{linenomath} where 0 < ω < π, subject to various non-local boundary conditions defined in terms of the Riemann–Stieltjes integrals. We prove the existence and multiplicity of positive solutions for these boundary value problems in both resonant and non-resonant cases. We discuss the resonant case by making a shift and considering an equivalent non-resonant problem.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089511000590