Conditions for the solvability of singular boundary value problems

Boundary Value Problems with Singular Boundary Conditions

Singular boundary conditions are formulated for non-selfadjoint Sturm-Liouville operators with singularities and turning points. For boundary value problems with singular boundary conditions properties of the spectrum are studied and the completeness of the system of root functions is proved.

Boundary value problems with regular singularities and singular boundary conditions

where skm are real numbers, pk0(t) ∈ C2[a,b], p00(t)p20(t) = 0, p00(t)/p20(t) > 0 for t ∈ [a,b]. Let s2m < s0m + 2, s2m ≤ s1m + 2, m = 0,1, that is, we consider the case of so-called regular singularities. Operators with irregular singularities possess different qualitative properties and require different investigations. Since the solutions of (1.1) may have singularities at the endpoints of t...

Solvability of Nonlocal Fractional Boundary Value Problems

Solvability of discrete Neumann boundary value problems

In this article we gain solvability to a nonlinear, second-order difference equation with discrete Neumann boundary conditions. Our methods involve new inequalities on the right-hand side of the difference equation and Schaefer’s Theorem in the finite-dimensional space setting. © 2006 Elsevier Inc. All rights reserved.

Solvability of Discrete Neumann Boundary Value Problems

In this article we gain solvability to a nonlinear, second-order difference equation with discrete Neumann boundary conditions. Our methods involve new inequalities on the right-hand side of the difference equation and Schaefer’s theorem in the finitedimensional space setting. Running Head: Discrete BVPs AMS Subject Code: 39A12, 34B15 Corresponding Author: C C Tisdell