Special Issue in honor of John W. Neuberger. Electron. J. Diff. Eqns., Special Issue 02 (2023), pp. 87-100.

Regular solutions to elliptic equations

Alfonso Castro, Jon Jacobsen

Abstract:
A review of results and techniques on the existence of regular radial solutions to second order elliptic boundary value problems driven by linear and quasilinear operators is presented. Of particular interest are results where the solvability of a given elliptic problem can be analyzed by the relationship between the spectrum of the operator and the behavior of the nonlinearity near infinity and at zero. Energy arguments and Pohozaev type identities are used extensively in that analysis. An appendix with a proof of the contraction mapping principle best suited for using continuous dependence to ordinary differential equations on initial conditions is presented. Another appendix on the phase plane analysis as needed to take advantage of initial conditions is also included. For studies on singular solutions the reader is referred to Ardila et al., Milan J. Math (2014) and references therein.

Published March 27, 2023.
Math Subject Classifications: 3502, 35J25, 34B16, 34B32.
Key Words: Nonlinear elliptic equation; radial solution; regular radial solution; singular radial solution; bifurcation analysis; Pohozaev identity; shooting method; superlinear nonlinearity; subcritical nonlinearity; sub-super critical nonlinearity; jumping nonlinearity
DOI: https://doi.org/10.58997/ejde.sp.02.c2

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Alfonso Castro
Department of Mathematics
Harvey Mudd College
Claremont CA 91711, USA
email: castro@hmc.edu
Jon Jacobsen
Department of Mathematics
Harvey Mudd College
Claremont CA 91711, USA
email: jacobsen@hmc.edu

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