Positive solutions for boundary value problem of sixth-order elastic beam equation

Abstract

In this paper, we study the existence of positive solutions for boundary value problem of sixth-order elastic beam equation of the form −u (6) The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. We give sufficient conditions that allow us to obtain the existence of positive solution. The main tool used in the proof is the Leray-Schauder nonlinear alternative and Leray-Schauder fixed point theorem. As an application, we also give example to illustrate the results obtained.

Comparative Study of Some Fixed-Point Methods in the Generation of Julia and Mandelbrot Sets

“…Output: sketched Mandelbrot set. (1) for a 0 ∈ A do (2) R-convergence condition for proposed method (3) m � 0 (4) z 0 -initial guess for Q a 0 (5) while m ≤ K do (6) Proposed iterative method (7) if |z m+1 | > R then (8) break ( 9) number of bulbs in different sizes, but if we magnify any bulb of image, it reflects the shape of whole image. In the generation of graphs in Figures 22-24, we change input Example 6. e last example demonstrates the ochto Mandelbrot sets for a polynomial Q(z) � z 8 + a 0 , where a 0 ∈ C in the orbits of M, M * , and K-iterative methods, respectively.…”

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On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h -Convex Functions

“…Many researchers in the last three decades are studying fractional calculus [8][9][10][11][12]. Some researchers deduced that it is essential to define new fractional derivatives with different singular or nonsingular kernels in order to provide more sufficient area to model more real-world problems in different fields of science and engineering [13][14][15][16][17][18][19].…”