Differential and Integral Equations

On non-monotone approximation schemes for solutions of the second order differential equations

Maria Dobkevich

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Abstract

The problem $$ \hskip 60pt u_{rr}+f(u)=0,\quad u_r(0)=0,\quad u(b)=0 \hskip 60pt {(P)} $$ arises when considering radially symmetric solutions of the problem $$ \Delta u+\varphi(u)=0,\quad u=0, \quad x\in\partial\Omega . $$ The problem (P) is solvable if the upper and lower functions $\alpha$ and $\beta$ exist. Then there exist solutions $u^*$ and $u_*$ (the maximal and minimal solutions), which can be approximated by monotone sequences of solutions of equation (P). Mostly solutions of (P) are of oscillatory types, and they cannot be approximated by monotone sequences. In this article we provide results on non-monotone approximations of solutions of the problem (P).

Article information

Source
Differential Integral Equations, Volume 26, Number 9/10 (2013), 1169-1178.

Dates
First available in Project Euclid: 3 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1372858570

Mathematical Reviews number (MathSciNet)
MR3100085

Zentralblatt MATH identifier
1299.34045

Subjects
Primary: 34B15: Nonlinear boundary value problems

Citation

Dobkevich, Maria. On non-monotone approximation schemes for solutions of the second order differential equations. Differential Integral Equations 26 (2013), no. 9/10, 1169--1178. https://projecteuclid.org/euclid.die/1372858570


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