Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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POSITIVE SOLUTIONS OF NONLINEAR m-POINT BVP FOR AN INCREASING HOMEOMORPHISM AND POSITIVE HOMOMORPHISM ON TIME SCALES

  • Han, Wei (Department of Mathematics, North University of China) ;
  • Jin, Zhen (Department of Mathematics, North University of China) ;
  • Zhang, Guang (School of Science, Tianjin University of Commerce)
  • Received : 2009.09.24
  • Accepted : 2009.10.27
  • Published : 2010.09.30
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Abstract

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $({\phi}(u^{\Delta}))^{\nabla}+a(t)f(t,\;u(t))=0$, t $\in$ (0, T), $u(0)=\sum\limits^{m-2}_{i=1}a_iu(\xi_i)$, $\phi(u^{\Delta}(T))=\sum\limits^{m-2}_{i=1}b_i{\phi}(u^{\Delta}(\xi_i))$, where $\phi$ : R $\rightarrow$ R is an increasing homeomorphism and positive homomorphism and ${\phi}(0)=0$. In [27], we obtained the existence results of the above problem for an increasing homeomorphism and positive homomorphism with sign changing nonlinearity. The purpose of this paper is to supplement with a result in the case when the nonlinear term f is nonnegative, and the most point we must point out for readers is that there is only the p-Laplacian case for increasing homeomorphism and positive homomorphism due to the sign restriction. As an application, one example to demonstrate our results are given.

Keywords

References

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