DOI QR코드

DOI QR Code

NONTRIVIAL SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

Guo, Yingxin

  • 발행 : 2010.01.31

초록

In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem(BVP) $-D_0^{\alpha}+u(t)=\lambda[f(t, u(t))+q(t)]$, 0 < t < 1 u(0) = u(1) = 0, where $\lambda$ > 0 is a parameter, 1 < $\alpha$ $\leq$ 2, $D_{0+}^{\alpha}$ is the standard Riemann-Liouville differentiation, f : [0, 1] ${\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is continuous, and q(t) : (0, 1) $\rightarrow$ [0, $+\infty$] is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when $\lambda$ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.

키워드

standard Riemann-Liouville differentiation;fractional differential equation;boundary-value problem;nontrivial solution;Leray-Schauder nonlinear alternative

참고문헌

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피인용 문헌

  1. Limit properties of positive solutions of fractional boundary value problems vol.219, pp.5, 2012, https://doi.org/10.4134/BKMS.2010.47.1.081
  2. The existence of positive solutions of singular fractional boundary value problems vol.62, pp.3, 2011, https://doi.org/10.4134/BKMS.2010.47.1.081
  3. Existence of solutions for nonlinear fractional q-difference equations with Riemann-Liouville type q-derivatives vol.47, pp.1-2, 2015, https://doi.org/10.4134/BKMS.2010.47.1.081
  4. Nontrivial solutions for a fractional boundary value problem vol.2013, pp.1, 2013, https://doi.org/10.4134/BKMS.2010.47.1.081
  5. Fractional boundary value problems with singularities in space variables vol.71, pp.4, 2013, https://doi.org/10.4134/BKMS.2010.47.1.081
  6. New computational techniques for solving nonlinear problems using g -fractional differential operator vol.330, 2018, https://doi.org/10.4134/BKMS.2010.47.1.081
  7. Existence and uniqueness of nontrivial solutions for eigenvalue boundary value problem of nonlinear fractional differential equation vol.60, pp.2, 2014, https://doi.org/10.4134/BKMS.2010.47.1.081