In this study, we consider the eigenvalue problems of fourth-order elastic beam equations. By using Avery and Peterson’s fixed point theory, we prove the existence of symmetric positive solutions for four-point boundary value problem (BVP). After this, we show that there is at least one positive solution by applying the fixed point theorem of Guo-Krasnosel’skii.
In this paper, we construct a new method for inextensible flows of spacelike curves in Minkowski space-time. Using the Frenet frame of the given curve, we present partial differential equations and we obtain solitions some of this equations. We give some characterizations for curvatures of a spacelike curve in Minkowski space-time.
In this paper an inverse problemwhere p are integrable on 0, 1 and satisfy the symmetry conditions p x p1 x almost everywhere in the interval 0 x 1. We reconstruct the potential of the inverse Sturm Liouville problem's solution is obtain for finite interval with symmetric potential.
In this article, the Sinh–Gordon function method and sub-equation method are used to construct traveling wave solutions of modified equal width equation. Thanks to the proposed methods, trigonometric soliton, dark soliton, and complex hyperbolic solutions of the considered equation are obtained. Common aspects, differences, advantages, and disadvantages of both analytical methods are discussed. It has been shown that the traveling wave solutions produced by both analytical methods with different base equations have different properties. 2D, 3D, and contour graphics are offered for solutions obtained by choosing appropriate values of the parameters. To evaluate the feasibility and efficacy of these techniques, a nonlinear evolution equation was investigated, and with the help of symbolic calculation, these methods have been shown to be a powerful, reliable, and effective mathematical tool for the solution of nonlinear partial differential equations.
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