On the Nonlinear Differential Equation for Beam Deflection: EI d 2 y / dx 2 = M ( x ) [ 1 + ( dy / dx ) 2 ] 3 ⁄ 2

1955 ◽  
Vol 22 (2) ◽  
pp. 245-248
Author(s):  
E. J. Scott ◽  
D. R. Carver
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Nonlinear Differential Equation ◽  
Beam Deflection ◽  
Beam Equation ◽  
Nonlinear Beam ◽  
Independent Variable ◽  
The Moment

Abstract A general solution of the nonlinear beam equation is given for all problems in which the moment can be expressed as a function of the independent variable alone.

scholarly journals Behaviour of the Kramer Radiating Star

1997 ◽  
Vol 50 (5) ◽  
pp. 959 ◽  
Author(s):  
S. D. Maharaj ◽  
M. Govender
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Nonlinear Differential Equation ◽  
Special Functions ◽  
Second Order ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Exterior Solution ◽  
Order Nonlinear Differential Equation ◽  
Radiating Star

We study the behaviour of the model for a radiating star proposed by Kramer. The evolution of the model is governed by a second order nonlinear differential equation. The general solution of this equation is expressed in terms of elementary and special functions. This completes the solution of the Einstein field equations for the interior of the star. The model matches smoothly to the Vaidya exterior solution and the condition p = qB is satisfied at the boundary. We briefly study the thermodynamics of the model and indicate the difficulty in specifying the temperature explicitly.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.

scholarly journals The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Xianzhen Zhang ◽  
Zuohua Liu ◽  
Hui Peng ◽  
Xianmin Zhang ◽  
Shiyong Yang
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
General Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Order System ◽  
Impulsive Systems ◽  
Fractional Differential ◽  
Noninstantaneous Impulses

Based on some recent works about the general solution of fractional differential equations with instantaneous impulses, a Caputo-Hadamard fractional differential equation with noninstantaneous impulses is studied in this paper. An equivalent integral equation with some undetermined constants is obtained for this fractional order system with noninstantaneous impulses, which means that there is general solution for the impulsive systems. Next, an example is given to illustrate the obtained result.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

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