Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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POSITIVE SOLUTIONS FOR NONLINEAR m-POINT BVP WITH SIGN CHANGING NONLINEARITY ON TIME SCALES

  • HAN, WEI (Department of Mathematics, North University of China) ;
  • REN, DENGYUN (Department of Mathematics, North University of China)
  • Received : 2017.02.27
  • Accepted : 2017.07.20
  • Published : 2017.09.30
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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 $$u^{{\Delta}{\nabla}}(t)+a(t)f(t,u(t))=0,\;t{\in}(0,T),\;{\beta}u(0)-{\gamma}u^{\Delta}(0)=0,\;u(T)={\sum_{i=1}^{m-2}}\;a_iu({\xi}_i),\;m{\geq}3$$, where $a(t){\in}C_{ld}((0,T),\;[0,+{\infty}))$, $f{\in}C([0,T]{\times}[0,+{\infty}),\;(-{\infty},+{\infty}))$, the nonlinear term f is allowed to change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. In particular, our criteria generalize and improve some known results [15] and the obtained conditions are different from related literature [14]. As an application, an example to demonstrate our results is given.

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References

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