The fundamental solution of an operator-differential equation with singular boundary condition

2011 ◽  
Vol 179 (2) ◽  
pp. 261-272
Author(s):  
Aleksandr M. Kholkin
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fundamental Solution ◽  
Singular Boundary ◽  
Operator Differential Equation ◽  
Singular Boundary Condition

On the Continuous Spectra of Singular Boundary Value Problems

1954 ◽  
Vol 6 ◽  
pp. 420-426 ◽  
Author(s):  
C. R. Putnam
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Boundary Value ◽  
Homogeneous Boundary Condition ◽  
Continuous Functions ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Image Position ◽  
Type 3 ◽  
Point Type

Suppose that p(t) > 0, that both p(t) and f(t) are continuous functions on the half-line 0 ≤ t < ∞, and that λ denotes a real parameter. Only real-valued functions will be considered in this paper. Let the differential equation,be of the limit-point type (3, p. 238), so that (1) and a linear homogeneous boundary condition, 0 ≤ α < π,determine a boundary value problem on 0 ≤ t < ∞ for every fixed α.

The solvability of an elliptic system under a singular boundary condition

2006 ◽  
Vol 136 (3) ◽  
pp. 509-546 ◽  
Author(s):  
J. García-Melián ◽  
J. Sabina de Lis ◽  
R. Letelier-Albornoz
Keyword(s):  
Boundary Condition ◽  
Elliptic System ◽  
Positive Solutions ◽  
Detailed Account ◽  
Singular Boundary ◽  
Dimensional Problem ◽  
One Dimensional ◽  
All Solutions ◽  
The One ◽  
Singular Boundary Condition

In this work we are considering both the one-dimensional and the radially symmetric versions of the elliptic system Δu = vp, Δv = uq in Ω, where p, q > 0, under the boundary condition u|∂Ω = +∞, v|∂Ω = +∞. It is shown that no positive solutions exist when pq ≤ 1, while we provide a detailed account of the set of (infinitely many) positive solutions if pq > 1. The behaviour near the boundary of all solutions is also elucidated, and symmetric solutions (u, v) are completely characterized in terms of their minima (u(0), v(0)). Non-symmetric solutions are also deeply studied in the one-dimensional problem.

scholarly journals Quenching for a Non-Newtonian Filtration Equation with a Singular Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Xiliu Li ◽  
Chunlai Mu ◽  
Qingna Zhang ◽  
Shouming Zhou
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Time ◽  
Singular Boundary ◽  
Quenching Rate ◽  
Filtration Equation ◽  
Laplacian Equation ◽  
Singular Boundary Condition

This paper deals with a nonlinearp-Laplacian equation with singular boundary conditions. Under proper conditions, the solution of this equation quenches in finite time and the only quenching point thatisx=1are obtained. Moreover, the quenching rate of this equation is established. Finally, we give an example of an application of our results.

Boundary behavior of large solutions to a class of Hessian equations

2020 ◽  
pp. 1-16
Author(s):  
Ling Mi ◽  
Chuan Chen
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Nonlinear Term ◽  
Boundary Behavior ◽  
Singular Boundary ◽  
Structure Condition ◽  
Hessian Equation ◽  
Large Solutions ◽  
Hessian Equations ◽  
Singular Boundary Condition

In this paper, we consider the m-Hessian equation S m [ D 2 u ] = b ( x ) f ( u ) > 0 in Ω, subject to the singular boundary condition u = ∞ on ∂ Ω. We give estimates of the asymptotic behavior of such solutions near ∂ Ω when the nonlinear term f satisfies a new structure condition.

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