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- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제35권 제5호
- 발행연도
- 2017.1
- 수록면
- 551 - 563 (13page)
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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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참고문헌 (16)
참고문헌 신청
R.P. Agarwal / 2001 / Nonlinear boundary value Problems on time scales / Nonl. Anal 44:527~535
R.P. Agarwal / 2003 / Half-linear dynamic equations, Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday / Kluwer Academic Publishers :1~57
D.R. Anderson / 2002 / Solutions to second-order three-point problems on time scales / J. Differ. Equ. Appl 8:673~688
F.M. Atici / 2002 / On Green’n functions and positive solutions for boundary value problems on time scales / J. Comput. Anal. Math 141:75~99
B. Aulbach / 2004 / Integration on measure chain / proc. of the Sixth Int. Conf. on Difference Equations, CRC :239~252
R.P. Agarwal / 2003 / Half-linear dynamic equations, Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday / Kluwer Academic Publishers :1~57
D.R. Anderson / 2002 / Solutions to second-order three-point problems on time scales / J. Differ. Equ. Appl 8:673~688
F.M. Atici / 2002 / On Green’n functions and positive solutions for boundary value problems on time scales / J. Comput. Anal. Math 141:75~99
B. Aulbach / 2004 / Integration on measure chain / proc. of the Sixth Int. Conf. on Difference Equations, CRC :239~252
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