ON THE SOLVABILITY OF A THIRD-ORDER INTEGRAL m-POINT RESONANT BOUNDARY VALUE PROBLEM ON THE HALF-LINE WITH TWO DIMENSIONAL KERNEL

Abstract

Existence results for a resonant third-order integral m-point boundary value problem on the half-line with dimension of the kernel of the linear differential operator equal to two are established. The tools that will be employed in this work are the Mawhin's coincidence degree theory, relevant algebraic methods and operators. An example will also be used to illustrate our result.

On the Solvability of a Resonant Third-Order Integral m-Point Boundary Value Problem on the Half-Line

“…under the resonant condition ∑ m−1 i=1 α i = 2 which is different from ours. For other literature on resonant multipoint boundary value problems on the half-line, see [10][11][12][13][14]. Motivated by the results mentioned above, we study the existence of solutions for the resonant third-order boundary value problem with integral and m-point boundary conditions on the half-line.…”