Results 1 to 10 of about 13,731,074 (335)

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
The author proves that for \(1< p0\). This completes the results obtained before by \textit{Y. Li} and \textit{W.-M. Ni} [Arch. Ration. Mech. Anal. 108, No. 2, 175-194 (1989; Zbl 0705.35039); ibid. 118, No. 3, 223-243 (1992; Zbl 0764.35014)].
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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On Positive Solutions of Semilinear Elliptic Equations [PDF]

Proceedings of the American Mathematical Society, 1987
This paper is concerned with necessary conditions for the existence of positive solutions of the semilinear problem Δ u + f ( u ) = 0 , x ∈ Ω , u = 0 , x ∈ ∂ Ω \Delta u + f(u) = 0,x \in \Omega ,u = 0,x ...
E. N. Dancer, Klaus Schmitt
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Elliptic equations without positive solutions

Journal of Differential Equations, 1985
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Thomas T. Read
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The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation [PDF]

Advanced Nonlinear Studies, 2022
We consider the existence and nonexistence of the positive solution for the following Brézis-Nirenberg problem with logarithmic perturbation: − Δ u = ∣ u ∣ 2 ∗ − 2 u + λ u + μ u log u 2 x ∈ Ω , u = 0 x ∈ ∂ Ω , \left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{
Yinbin Deng, Qihan He, Yiqing Pan, X. Zhong   +3 more
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Maximal and minimal iterative positive solutions for p-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term

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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A positive solution for an anisotropic $ (p,q) $-Laplacian

Discrete and Continuous Dynamical Systems. Series A, 2022
Here, the anisotropic \begin{document}$ (p, q) $\end{document}-Laplacian \begin{document}$ - \sum\limits_{i = 1}^N\frac{\partial}{\partial x_i}\left( \left|\frac{\partial u}{\partial x_i}\right|^{p_i-2}\frac{\partial u}{\partial x_i}\right) - \sum ...
A. Razani, G. Figueiredo
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