Results 1 to 10 of about 5,321,104 (325)
On Positive Solutions of the Heat Equation [PDF]
Nagoya Mathematical Journal, 1967 Consider the positive and twice continuously differentiable solutions u of the heat equationin an open t-strip Ω = Rn×(0,T) for some T>0, where Rn is the n-dimensional Euclidean space.In this note, we prove a theorem of Fatou type on u and, as its application, the uniqueness theorem for the Cauchy problem of ( 1 ).
Masasumi Kato
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Positive Solutions of Positive Linear Equations [PDF]
Proceedings of the American Mathematical Society, 1972 Let B B be a real vector lattice and a Banach space under a semimonotonic norm. Suppose T T is a linear operator on B B which is positive and eventually compact, y y is a positive vector, and λ \lambda is a positive real. It is shown that (
Paul D. Nelson
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Positive solutions of the diophantine equation
International Journal of Mathematics and Mathematical Sciences, 1982 Integral solutions of x3+λy+1−xyz=0 are observed for all integral λ. For λ=2 the 13 solutions of the equation in positive integers are determined. Solutions of the equation in positive integers were previously determined for the case λ=1.
W. R. Utz
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On the positive solutions of the Matukuma equation [PDF]
Duke Mathematical Journal, 1993 where p > 1 and u > 0 is the gravitational potential with f R3 (uP/4n(1 + Ix12» dx representing the total mass. His aim was to improve a model given earlier in 1915 by A. S. Eddington. (See [NY1,2] for a more detailed history of these two models.) Since the Matukuma equation (1.1)is rotationally invariant, the structure of positive radial solutions u(r,
Yi Li
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Positive solutions of the heat equation [PDF]
Bulletin of the American Mathematical Society, 1963 D. V. Widder
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AIMS Mathematics, 2021 In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function
Limin Guo, Lishan Liu, Ying Wang
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On Positivity Sets for Helmholtz Solutions
Vietnam Journal of Mathematics, 2023 AbstractWe address the question of finding global solutions of the Helmholtz equation that are positive in a given set. This question arises in inverse scattering for penetrable obstacles. In particular, we show that there are solutions that are positive on the boundary of a bounded Lipschitz domain.
Pu-Zhao Kow +2 more
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Real positive solutions of operator equations $ AX = C $ and $ XB = D $
AIMS Mathematics, 2023 In this paper, we mainly consider operator equations $ AX = C $ and $ XB = D $ in the framework of Hilbert space. A new representation of the reduced solution of $ AX = C $ is given by a convergent operator sequence.
Haiyan Zhang , Yanni Dou , Weiyan Yu
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Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
Entropy, 2022 This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term −Δu=f(x,u,∇u) on Ω restricted by the boundary condition u|∂Ω=0, where Ω is a bounded domain in RN with sufficiently smooth boundary ∂Ω, N≥2, and f:Ω¯×R×
Yongxiang Li, Weifeng Ma
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Algebraic Systems with Positive Coefficients and Positive Solutions
Mathematics, 2022 The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichlet problems, difference equations, boundary value ...
Ana Maria Acu +2 more
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