NON-EXISTENCE OF SOLUTIONS FOR TWO-POINT FRACTIONAL AND THIRD-ORDER BOUNDARY-VALUE PROBLEMS

作者：Karakostas George L^*

来源：Electronic Journal of Differential Equations, 2013, 152.

• Third order differential equation
• two-point boundary-value problem
• fractional boundary condition
• nonexistence of solutions

In this article, we provide sufficient conditions for the non-existence of solutions of the boundary-value problems with fractional derivative of order alpha is an element of (2, 3) in the Riemann-Liouville sense %26lt;br%26gt;D-0+(alpha) x(t) + lambda alpha(t)f(x(t)) = 0, t is an element of (0, 1), %26lt;br%26gt;x(0) = x%26apos;(0) = x%26apos;(1) = 0, %26lt;br%26gt;and in the Caputo sense %26lt;br%26gt;(C) D(alpha)x(t) + f(t, x(t)) = 0, t is an element of (0, 1), %26lt;br%26gt;x(0) = x%26apos;(0) = 0, x(1) = lambda integral(1)(0) x(s)ds; %26lt;br%26gt;and for the third-order differential equation %26lt;br%26gt;x%26apos;%26apos;%26apos;(t) + (Fx)(t) = 0, a.e. t is an element of [0, 1], %26lt;br%26gt;associated with three among the following six conditions %26lt;br%26gt;x(0) = 0, x(1) = 0, x%26apos;(0) = 0, x%26apos;(1) = 0, x %26apos;%26apos;(0) = 0, x %26apos;%26apos;(1) = 0. %26lt;br%26gt;Thus, fourteen boundary-value problems at resonance and six boundary-value problems at non-resonanse are studied. Applications of the results are, also, given.

• 出版日期2013-6-28