On the well-posedness of a boundary value problem for a class of fourth-order operator-differential equations

2012 ◽  
Vol 48 (4) ◽  
pp. 596-598 ◽  
Author(s):  
A. R. Aliev ◽  
A. S. Mohamed
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Well Posedness ◽  
Order Operator

scholarly journals Iterative method for solving the second boundary value problem (BVP) for Biharmonic type equation

2016 ◽  
Vol 14 (4) ◽  
pp. 66-72
Author(s):  
Đặng Quang Á
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Equation ◽  
Second Order ◽  
Second Order Equations

Solving BVPs for the fourth order differential equations by the reduction of them to BVPs for the  second order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by  ourselves in recent works, we construct iterative method for the second BVP for  biharmonic type equation. The convergence rate of  the method is established.

scholarly journals Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Panos K. Palamides ◽  
Alex P. Palamides
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Boundary Value ◽  
Point Boundary ◽  
Negative Solution ◽  
Order Four ◽  
The Continuum

We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the continuum property (connectedness and compactness) of the solutions funnel (Kneser's Theorem), combined with the corresponding vector field.

scholarly journals Integro-differential systems with variable exponents of nonlinearity

2017 ◽  
Vol 15 (1) ◽  
pp. 859-883 ◽  
Author(s):  
Oleh Buhrii ◽  
Nataliya Buhrii
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Existence Theorem ◽  
Fourth Order ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Exponents ◽  
Differential Systems ◽  
Initial Boundary Value

Abstract Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.

scholarly journals Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Dang Quang A. ◽  
Nguyen Van Thien
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Equation ◽  
Numerical Examples ◽  
Optimal Value ◽  
Second Order Equations

Solving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.

scholarly journals A remark on elliptic differential equations on manifold

2020 ◽  
Vol 99 (3) ◽  
pp. 75-85
Author(s):  
A. Ashyralyev ◽  
◽  
Y. Sozen ◽  
F. Hezenci ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Elliptic Type ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Elliptic Boundary Value

For elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also DirichletBitsadze-Samarskii type nonlocal boundary value problem on manifolds, in H¨older spaces. In addition, in various H¨older norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds.

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