Expansions in terms of Papkovich–Fadle eigenfunctions in the problem for a half‐strip with stiffeners

2021 ◽  
Author(s):  
Mikhail D. Kovalenko ◽  
Irina V. Menshova ◽  
Alexander P. Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Half Strip

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

Inhomogeneous Problem of the Theory of Elasticity in a Half-Strip. Exact Solution

2020 ◽  
Vol 55 (6) ◽  
pp. 784-790
Author(s):  
M. D. Kovalenko ◽  
I. V. Menshova ◽  
A. P. Kerzhaev ◽  
G. Yu
Keyword(s):  
Exact Solution ◽  
Theory Of Elasticity ◽  
Inhomogeneous Problem ◽  
Half Strip

scholarly journals Multiplicity results for some nonlinear elliptic problems

2004 ◽  
Vol 76 (2) ◽  
pp. 247-268
Author(s):  
Kuan-Ju Chen
Keyword(s):  
Ground State ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Ground State Solution ◽  
State Solution ◽  
Energy Solution ◽  
Nonlinear Elliptic Problems ◽  
Multiplicity Results ◽  
Nonlinear Elliptic ◽  
Half Strip

AbstractIn this paper, first, we study the existence of the positive solutions of the nonlinear elliptic equations in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. We assert that if there exists a (PS)c-sequence with c belonging to a suitable interval depending by the equation, then a ground state solution and a positive higher energy solution exist, too. Next, we study the upper half strip with a hole. In this case, the ground state solution does not exist, however there exists at least a positive higher energy solution.

scholarly journals On the Limit of the Modulus of a Bounded Regular Function

1964 ◽  
Vol 14 (1) ◽  
pp. 21-24 ◽  
Author(s):  
N. A. Bowen
Keyword(s):  
Complex Plane ◽  
Regular Function ◽  
Half Strip ◽  
Image Position

M. L. Cartwright has given ((2), 180–181) the following theorem, together with a neat proof of it.Theorem C.Suppose that f(z) is regular andin the half-strip Sof the complex plane.Suppose also that for some constant α in α<a<βas y→∞. Then for every δ>0.uniformly asy→∞ for α+δ≦x≦β–δ.

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