Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE EXISTENCE OF TWO POSITIVE SOLUTIONS FOR $m$-POINT BOUNDARY VALUE PROBLEM WITH SIGN CHANGING NONLINEARITY

  • Liu, Jian (School of Mathematical Sciences, Qufu Normal University)
  • Received : 2011.08.09
  • Accepted : 2011.10.10
  • Published : 2012.05.30
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Abstract

In this paper, the existence theorem of two positive solutions is established for nonlinear m-point boundary value problem by using an inequality for the following third-order differential equations $$({\phi}(u^{\prime\prime}))^{\prime}+a(t)f(t,u(t))=0,\;t{\in}(0,1)$$, $${\phi}(u^{\prime\prime}(0))=\sum^{m-2}_{i=1}a_i{\phi}(u^{\prime\prime}({\xi}_i)),\;u^{\prime}(1)=0,\;u(0)=\sum^{m-2}_{i=1}b_iu({\xi}_i)$$, where ${\phi}:R{\rightarrow}R$ is an increasing homeomorphism and homomorphism and $\phi(0)=0$. The nonlinear term f may change sign, as an application, an example to demonstrate our results is given.

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References

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