Existence of Positive Solutions for a Pertubed Fourth-Order Equation

Mohammad Reza Heidari Tavani, Abdollah Nazari

In this paper, a special type of fourth-order differential equations with a perturbed nonlinear term and some boundary conditions is considered which is very important in mechanical engineering. Therefore, the existence of a non-trivial solution for such equations is very important. Our goal is to ensure at least three weak solutions for a class of perturbed fourth-order problems by applying certain conditions to the functions that are available in the differential equation (problem \eqref{1}). Our approach is based on variational methods and critical point theory. In fact, using a fundamental theorem that is attributed to Bonanno, we get some important results. Finally, for some results, an example is presented.