Estimates of solutions of certain fourth-order equations of composite type

1977 ◽  
Vol 17 (4) ◽  
pp. 555-559
Author(s):  
P. E. Berkhin
Keyword(s):  
Fourth Order ◽  
Estimates Of Solutions ◽  
Composite Type ◽  
Fourth Order Equations

scholarly journals WEAK SOLUTIONS OF BOUNDARY VALUE PROBLEMS IN NONTUBE DOMAINS FOR FOURTH-ORDER EQUATIONS OF COMPOSITE TYPE

2011 ◽  
Vol 16 (3) ◽  
pp. 498-508
Author(s):  
Victor Korzyuk ◽  
Olga Kovnatskaya
Keyword(s):  
Functional Analysis ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Composite Type ◽  
Fourth Order Equations

In the paper existence and uniqueness of weak solutions of boundary value problems in nontube domains for fourth-order equations of composite type are proved by methods of functional analysis.

scholarly journals Asymptotic theory for a critical case for a general fourth-order differential equation

1998 ◽  
Vol 21 (3) ◽  
pp. 479-488
Author(s):  
A. S. A. Al-Hammadi
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Critical Case ◽  
Asymptotic Theory ◽  
Order Differential Equation ◽  
Fourth Order Equations ◽  
Fourth Order Differential Equation

In this paper we identify a relation between the coefficients that represents a critical case for general fourth-order equations. We obtained the forms of solutions under this critical case.

Some methods for determining acceleration and tilt by use of pendulums and accelerometers

1973 ◽  
Vol 63 (1) ◽  
pp. 1-7
Author(s):  
Hugh Bradner ◽  
Michael Reichle
Keyword(s):  
Ground Motion ◽  
Fourth Order ◽  
Horizontal Displacement ◽  
Natural Period ◽  
Rotational Components ◽  
Fourth Order Equations ◽  
Special Case

abstract We consider the use of a system of horizontal and vertical pendulums to determine linear and rotational components of ground motion. Accelerometers can be viewed as a special case of pendulums. Fourth-order equations are always required for determining horizontal displacement unless the natural period of at least one sensor lies far below the passband of interest. Applications to guidance and to seismology are mentioned briefly.

Some nonexistence theorems for semilinear fourth-order equations

2018 ◽  
Vol 149 (03) ◽  
pp. 761-779 ◽  
Author(s):  
M. Á. Burgos-Pérez ◽  
J. García-Melián ◽  
A. Quaas
Keyword(s):  
Fourth Order ◽  
Exterior Domains ◽  
Order Problem ◽  
Previous Condition ◽  
Fourth Order Problem ◽  
Radially Symmetric Solutions ◽  
Image Position ◽  
Fourth Order Equations

AbstractIn this paper, we analyse the semilinear fourth-order problem ( − Δ)2 u = g(u) in exterior domains of ℝN. Assuming the function g is nondecreasing and continuous in [0, + ∞) and positive in (0, + ∞), we show that positive classical supersolutions u of the problem which additionally verify − Δu > 0 exist if and only if N ≥ 5 and $$\int_0^\delta \displaystyle{{g(s)}\over{s^{(({2(N-2)})/({N-4}))}}} {\rm d}s \lt + \infty$$ for some δ > 0. When only radially symmetric solutions are taken into account, we also show that the monotonicity of g is not needed in this result. Finally, we consider the same problem posed in ℝN and show that if g is additionally convex and lies above a power greater than one at infinity, then all positive supersolutions u automatically verify − Δu > 0 in ℝN, and they do not exist when the previous condition fails.

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