Existence of solutions to infinite elastic beam equations with unbounded nonlinearities

Abstract

This article concerns the existence of unbounded solutions to fourth-order boundary-value problem on the half-line with two-point boundary conditions. One-sided Nagumo condition plays a special role as it allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on the Schauder fixed point theorem and lower and upper solutions method. As an application, an example is given with non-ordered lower and upper solutions, to prove our results.

Keywords

• Half line problem
• Schauder fixed point theorem
• unbounded and nonordered upper and lower solutions
• one-sided Nagumo condition