Solvability of the boundary-value problem for a partial quasilinear differential equation of the fourth order

2010 ◽  
Vol 54 (12) ◽  
pp. 45-50 ◽  
Author(s):  
S. N. Timergaliev ◽  
I. R. Mavleev
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Quasilinear Differential Equation

scholarly journals A Comparison between the fourth order linear differential equation with its boundary value problem

2020 ◽  
Vol 99 (3) ◽  
pp. 18-25
Author(s):  
Karwan H.F. Jwamer ◽  
◽  
Rando R.Q. Rasul ◽  
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Linear Differential Equation ◽  
Fourth Order ◽  
Upper Bound ◽  
Boundary Value ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Linear Differential

In this paper, we study a fourth order linear differential equation. We found an upper bound for the solutions of this differential equation and also, we prove that all the solutions are in L4(0, ∞). By comparing these results we obtain that all the eigenfunction of the boundary value problem generated by this differential equation are bounded and in L4(0, ∞).

On one two-point BVP for the fourth order linear ordinary differential equation

2017 ◽  
Vol 24 (2) ◽  
pp. 265-275
Author(s):  
Sulkhan Mukhigulashvili ◽  
Mariam Manjikashvili
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Homogeneous Problem ◽  
Sufficient Conditions ◽  
Linear Ordinary Differential Equation ◽  
Point Boundary ◽  
Order Linear

AbstractIn this article we consider the two-point boundary value problem\left\{\begin{aligned} &\displaystyle u^{(4)}(t)=p(t)u(t)+h(t)\quad\text{for }% a\leq t\leq b,\\ &\displaystyle u^{(i)}(a)=c_{1i},\quad u^{(i)}(b)=c_{2i}\quad(i=0,1),\end{% aligned}\right.where {c_{1i},c_{2i}\in R}, {h,p\in L([a,b];R)}. Here we study the question of dimension of the space of nonzero solutions and oscillatory behaviors of nonzero solutions on the interval {[a,b]} for the corresponding homogeneous problem, and establish efficient sufficient conditions of solvability for the nonhomogeneous problem.

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