Multiple positive solutions to a fourth order boundary value problem


We study the existence, localization and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii’s compression-expansion theorem, and unilateral Harnack type inequalities.


Alberto Cabada
Instituto de Matematicas, Facultade de Matem aticas, Universidade de Santiago de Compostela, Santiago de Compostela, Galicia, Spain

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Lorena Saavedra
Instituto de Matematicas, Facultade de Matematicas, Universidade de Santiago de Compostela, Santiago de Compostela, Galicia, Spain

Stepan A. Tersian
Department of Mathematics, University of Ruse, 7017 Ruse, Bulgaria.
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 – Sofia, Bulgaria


Fourth-order differential equation; boundary-value problem; positive solution; critical point; fixed point.

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A. Cabada, R. Precup, L. Saavedra, S. Tersian, Multiple positive solutions to a fourth order boundary value problem, Electron. J. Differential Equations 2016 (2016), No. 254, 1-18.


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