Limit properties of positive solutions of fractional boundary value problems

作者：Stanek Svatoslav^*

来源：Applied Mathematics and Computation, 2012, 219(5): 2361-2370.

DOI：10.1016/j.amc.2012.09.008

• Fractional differential equation
• Functional boundary conditions
• Caputo fractional derivative
• Positive solution
• Leray-Schauder degree
• Borsuk antipodal theorem
• Limit properties of solutions

We investigate the sequence of fractional boundary value problems
(c)D(alpha n)u = Sigma(m)(k=1)a(k)(t)(c)D(mu k,n)u + f(t,u,u ',(c)D(beta n)u), u '(0) = 0, u(1) = Phi(u) - Lambda(u ')
where lim(n ->infinity)alpha(n) = 2; lim(n ->infinity)beta(n) = 1, lim(n ->infinity)mu(k,n) = 1; a(k) is an element of C[0,1] (k = 1, 2,...,m), f is an element of C[(0,1] x D), D subset of R-3, and Phi, Lambda: C[0,1] -> R are linear functionals. D-c is the Caputo fractional derivative. It is proved, by the Leray-Schauder degree theory, that for each n is an element of N the problem has a positive solution un, and that there exists a subsequence {u(n)'} of {u(n)} converging to a positive

• 出版日期2012-11-15