Local properties of solutions of a differential equation via normed linear spaces

DOI10.1080/09720502.1998.10700242zbMath0907.35007OpenAlexW2318331961WikidataQ115296550 ScholiaQ115296550MaRDI QIDQ4215660

Michael A. Karls, Frederick D. Gylys-Colwell

Publication date: 29 November 1998

Published in: Journal of Interdisciplinary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/09720502.1998.10700242

zbMATH Keywords

differentiable fixed-point theorem

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Cites Work

• Radial solutions of \(\Delta u+f(u)=0\) with prescribed numbers of zeros
• Ground states of \(-\Delta u=f(u)\) and the Emden-Fowler equation
• Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Symmetry and related properties via the maximum principle
• Nonlinear differential equations and dynamical systems
• Multidimensional nonlinear diffusion arising in population genetics
• Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
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