Existence of a solution to a nonlinear fourth-order boundary value problem with two parameters. (Chinese. English summary) Zbl 1174.34313
Summary: Using Leray-Schauder nonlinear alternative, an existence theorem is established for a class of nonlinear fourth-order boundary value problems with two parameters and all order derivatives, where the nonlinear term satisfies a linear growth condition. The problem describes the deformations of an elastic beam simply supported at both ends.
MSC:
34B08 | Parameter dependent boundary value problems for ordinary differential equations |
34B15 | Nonlinear boundary value problems for ordinary differential equations |