## Differential and Integral Equations

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

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

#### 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