Uniqueness of positive solutions for a class of fractional boundary value problems

作者：Xu Jiafa^*; Wei Zhongli; Dong Wei

来源：Applied Mathematics Letters, 2012, 25(3): 590-593.

DOI：10.1016/j.aml.2011.09.065

• Fractional boundary value problem
• Spectral radii
• Positive solution
• Fixed point index

The work is concerned with the existence and uniqueness of positive solutions for the following fractional boundary value problem:
{D(0+)(nu) u(t) + h(t)f(t, u(t)) = 0, 0 < t < 1, n - 1 < nu <= n,
u(0) = u'(0) = ... = u((n-2)) (0) = 0,
[D(0+)(alpha) u(t)](t=1) = 0, 1 <= alpha <= n - 2,
where n is an element of N and n > 3, and D(0+)(nu) is the standard Riemann-Liouville fractional derivative of order v. Our main results are formulated in terms of spectral radii of some related linear integral operators, and the nonlinearity f is considered to grow only sublinearly.

• 出版日期2012-3
• 单位山东建筑大学; 山东大学; 河北工程大学