On a discontinuous beam-type equation with deviating argument in the curvatureReport as inadecuate




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Boundary Value Problems

, 2016:180

First Online: 12 October 2016Received: 02 July 2016Accepted: 21 September 2016

Abstract

We deal with a nonlinear fourth-order equation where the linear part is given by the second derivative of an invertible second-order operator. The equation includes a deviating argument and the boundary conditions provide information as regards the behavior of the solution in an initial and a final interval. Some discontinuities are allowed in all the variables and we prove for this problem the existence of solutions lying between lower and upper solutions. With the extra assumption that the given second-order operator is inverse positive we prove the existence of extremal solutions. An example is also included in order to show the application of our results.

Keywordsfourth-order boundary value problems deviating arguments discontinuous equations lower and upper solutions MSC34B99  Download fulltext PDF



Author: Rubén Figueroa

Source: https://link.springer.com/







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