Results 1 to 10 of about 2,145,975 (237)
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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Positive Solutions of Difference Equations [PDF]
Proceedings of the American Mathematical Society, 1990 Proceedings of the American Mathematical ...
Philos, C. G., Sficas, Y. G.
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