# On the Solvability of Nonlinear Differential Equations Subject to Generalized Boundary Conditions

## TL;DR

This paper develops a framework for determining the solvability of nonlinear differential equations with generalized boundary conditions, simplifying the process of analyzing complex boundary value problems.

## Contribution

It introduces a new, straightforward set of conditions for the solvability of nonlinear scalar boundary value problems by reformulating them as operator equations.

## Key findings

- Provides a general strategy for boundary value problem analysis
- Establishes solvability conditions that are easy to verify
- Compares new results with previous related work

## Abstract

In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability of a large number of nonlinear scalar boundary value problems. We begin by giving our general strategy which involves the reformulation of our boundary value problem as an operator equation. We then proceed to establish our results and compare them to closely related previous work.