scholarly journals Boundary value problems for the mildly non-linear ordinary differential equation of the fourth order

1974 ◽  
Vol 19 (4) ◽  
pp. 216-231
Author(s):  
Helena Růžičková
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Linear Ordinary Differential Equation ◽  
Non Linear

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.

EXISTENCE THEOREMS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS

2004 ◽  
Vol 02 (01) ◽  
pp. 71-85 ◽  
Author(s):  
YUJI LIU ◽  
WEIGAO GE
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value ◽  
Growth Conditions ◽  
Point Boundary ◽  
Order Ordinary Differential Equation ◽  
Order Four

In this paper, we study four-point boundary value problems for a fourth-order ordinary differential equation of the form [Formula: see text] with one of the following boundary conditions: [Formula: see text] or [Formula: see text] Growth conditions on f which guarantee existence of at least three positive solutions for the problems (E)–(B1) and (E)–(B2) are imposed.

scholarly journals Initiation of thermal explosion by intense light: criticality dependence on data and parameters

1987 ◽  
Vol 28 (3) ◽  
pp. 287-295 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Steady State Solution ◽  
Linear Ordinary Differential Equation ◽  
Critical Parameters ◽  
Linear Parabolic Equation ◽  
Thermal Ignition ◽  
Non Linear ◽  
Intense Light

AbstractA model for thermal ignition by intense light is studied. The governing non-linear parabolic equation is linearized in a two-step manner with the aid of a non-linear ordinary differential equation which captures the salient features of the non-linear parabolic equation. The critical parameters are computed from the steady-state solution of the ordinary differential equation, which can be obtained without actually solving the equation. Comparison with available data shows that the present method yields good results.

scholarly journals The Collocation Method For Fourth Order Fuzzy Boundary Value Problems

2019 ◽  
Vol 21 (85) ◽  
pp. 1-10
Author(s):  
Rasha H.Ibraheem
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Fourth Order ◽  
Level Sets ◽  
Boundary Value ◽  
Method Of Solution ◽  
Α Level ◽  
Fuzzy Boundary Value Problems ◽  
Fuzzy Boundary

In this paper, the collocation method is considered to solve the nonhomogeneous  for fourth order fuzzy boundary value problems, In which the fuzziness appeared together in the boundary conditions and in the nonhomogeneous term of the differential equation. The method of solution depends on transforming the fuzzy problem to equivalent crisp problems using the concept of α-level sets.

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