Korean Journal of Mathematics

  • 제23권4호
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  • Pages.537-555
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  • 2015
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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EXISTENCE OF SOLUTION FOR A FRACTIONAL DIFFERENTIAL INCLUSION VIA NONSMOOTH CRITICAL POINT THEORY

  • YANG, BIAN-XIA (School of Mathematics and Statistics Lanzhou University) ;
  • SUN, HONG-RUI (School of Mathematics and Statistics Lanzhou University)
  • 투고 : 2015.08.24
  • 심사 : 2015.10.28
  • 발행 : 2015.12.30
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초록

This paper is concerned with the existence of solutions to the following fractional differential inclusion $$\{-{\frac{d}{dx}}\(p_0D^{-{\beta}}_x(u^{\prime}(x)))+q_xD^{-{\beta}}_1(u^{\prime}(x))\){\in}{\partial}F_u(x,u),\;x{\in}(0,1),\\u(0)=u(1)=0,$$ where $_0D^{-{\beta}}_x$ and $_xD^{-{\beta}}_1$ are left and right Riemann-Liouville fractional integrals of order ${\beta}{\in}(0,1)$ respectively, 0 < p = 1 - q < 1 and $F:[0,1]{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is locally Lipschitz with respect to the second variable. Due to the general assumption on the constants p and q, the problem does not have a variational structure. Despite that, here we study it combining with an iterative technique and nonsmooth critical point theory, we obtain an existence result for the above problem under suitable assumptions. The result extends some corresponding results in the literatures.

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참고문헌

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