Solvability of an m-Point Boundary Value Problem for Second Order Ordinary Differential Equations

On a Singular Second-Order Multipoint Boundary Value Problem at Resonance

“…In [1] Gupta et al studied the above equation when and have no singularity and ∑ = 1 (the resonance case) and when and have a singularity at = 1. We shall employ coincidence degree arguments in obtaining our results.…”

“…We shall employ coincidence degree arguments in obtaining our results. In this case, the methods used in [1,2] are not valid.…”

“…However to the best of our knowledge the corresponding problem for second-order differential equations at resonance and with a singularity had not received much attention in the literature. For recent results in these directions see [1,2,[4][5][6][7][8][9] and references therein.…”

Existence theorems for a second order m‐point boundary value problem at resonance

“…Accordingly, it seems that one can study the problem of existence of a solution for the boundary value problem (2) using the a priori estimates obtained for the three-point boundary value problem (1), as it was done in [2], [3], [4]. But here the m-point boundary value problem (2) [6] or [7].…”

A priori estimates and solvability of a non-resonant generalized multi-point boundary value problem of mixed Dirichlet-Neumann-Dirichlet type involving a p-Laplacian type operator

“…, n − 2. The study of multi-point boundary value problems for nonlinear second order ordinary differential equations was initiated by Il'in and Moiseev in [23], [24] who were motivated by the works of Bitsadze and Samarskiȋ on nonlocal linear elliptic boundary value problems, [2], [3], [4], and it has been the subject of many papers, see for example [5], [6], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [22], [25], [30] and [31]. More recently multipoint boundary value problems involving a p-Laplacian type operator or the more general operator −(ϕ(x ′ )) ′ have been studied in [1], [7], [8], [9], [10], [26], to mention just a few.…”