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Fourth-order boundary value problems model some kinds of deformations of an elastic beam. They have been studied by many authors via various methods, such as LeraySchauder continuation method, topological degree theory, shooting method, fixed point theorems on cones, critical point theory, the lower and upper solutions method or spectral theory.

 In this talk, we study the existence and multiplicity of positive solutions for the fourth order equations with integral conditions on the boundary.(For more see attached file)

References:

[1] A. Cabada and C. Fernández-Gómez, Constant sign solutions of two-point fourth order problems, Appl. Math. Comput., 263 (2015), 122–133.
[2] A. Cabada and R. Jebari, Multiplicity results for fourth order problems related to the theory of deformations beams, Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), 2, 489–505.