Geodesic
Existence of Positive Solutions for a Pertubed Fourth-Order Equation
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 4, p. 623

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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.
Classification : 34B15, 34B18, 58E05
Keywords: fourth-order equation, weak solution, critical point theory, variational methods 
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     author = {Mohammad Reza Heidari Tavani and Abdollah Nazari},
     title = {Existence of {Positive} {Solutions} for a {Pertubed} {Fourth-Order} {Equation}},
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Mohammad Reza Heidari Tavani; Abdollah Nazari. Existence of Positive Solutions for a Pertubed Fourth-Order Equation. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 4, p. 623 . http://geodesic.mathdoc.fr/item/KJM_2021_45_4_a9/