MULTIPLE POSITIVE SOLUTIONS OF RESONANT AND NON-RESONANT NON-LOCAL FOURTH-ORDER BOUNDARY VALUE PROBLEMS
MULTIPLE POSITIVE SOLUTIONS OF RESONANT AND NON-RESONANT NON-LOCAL FOURTH-ORDER BOUNDARY VALUE PROBLEMS
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DOI：
10.1017/s0017089511000590
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发表时间：
2011-12
影响因子：
0.5
通讯作者：
J. Webb;M. Zima
中科院分区：
文献类型：
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作者：
J. Webb;M. Zima
本文研究了形式为Begin{linenomath}${linenomath}$(T)-{\omega}^4u(T)=f(t，u(T))，\；；\Text{A.E.}，$$\end{linenomath}其中0<；ω<；π的正解的存在性。我们证明了这些边值问题在共振和非共振情况下正解的存在性和多解性。我们通过平移并考虑一个等价的非共振问题来讨论共振情况。
Abstract We study the existence of positive solutions for equations of the form \begin{linenomath}$$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.