Sufficient Conditions for Solvability of One Class of Neumann-Type Problems for the Polyharmonic Equation

2021 ◽  
Vol 61 (8) ◽  
pp. 1276-1288
Author(s):  
V. V. Karachik
Keyword(s):  
Sufficient Conditions ◽  
Polyharmonic Equation ◽  
Neumann Type

SOLVABILITY OF NEUMANN TYPE NON-HOMOGENEOUS MULTI-POINT BVP FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN

2009 ◽  
Vol 07 (03) ◽  
pp. 279-295
Author(s):  
YUJI LIU
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Point Boundary ◽  
Second Order Differential Equations ◽  
Neumann Type

We consider the following multi-point boundary value problems [Formula: see text] New sufficient conditions to guarantee the existence of at least one solution of the above mentioned BVP are established. Two examples are presented to illustrate the main result.

Stability and Instability of the Wave Equation Solutions in a Pulsating Domain

1998 ◽  
Vol 10 (07) ◽  
pp. 925-962 ◽  
Author(s):  
J. Dittrich ◽  
P. Duclos ◽  
N. Gonzalez
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
D’Alembert Equation ◽  
Stability And Instability ◽  
Unlimited Growth ◽  
Neumann Type ◽  
Finite Space ◽  
Space Interval

The behavior of energy is studied for the real scalar field satisfying d'Alembert equation in a finite space interval 0<x<a(t); the endpoint a(t) is assumed to move slower than the light and periodically in most parts of the paper. The boundary conditions are of Dirichlet and Neumann type. We give sufficient conditions for the unlimited growth, the boundedness and the periodicity of the energy E. The case of unbounded energy without infinite limit (0< lim inf t→+∞E(t) < lim sup t→+∞E(t)=+∞) is also possible. For the Neumann boundary condition, E may decay to zero as the time tends to infinity. If a is periodic, the solution is determined by a homeomorphism [Formula: see text] of the circle related to a. The behavior of E depends essentially on the number theoretical characteristics of the rotation number of [Formula: see text].

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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