FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 133-147

**Existence of solutions of certain quasilinear elliptic equations
in $$****R**^{N} without
conditions at infinity

G. I. Laptev

Abstract

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The paper deals with conditions for the existence of solutions of the
equations

$$-
å
_{i=1}^{n}D_{i}A_{i}(x,u,Du) +
A_{0}(x,u) = f(x),
x Î
**R**^{n},
considered in the whole space $$**R**^{n},
$n$³
2.
The functions $A$_{i}(x,u,
x), $i\; =\; 1,...,n$, $A$_{0}(x,u), and
$f(x)$ can
arbitrarily grow as $|x|\; \to $¥.
These functions satisfy generalized conditions of the monotone
operator theory in the arguments $u$Î **R** and
$$x
Î
**R**^{n}.
We prove the existence theorem for a solution $u$Î
W_{loc}^{1,p}(**R**^{n})
under the condition $p\; >\; n$.

Location: http://mech.math.msu.su/~fpm/eng/k06/k064/k06409h.htm

Last modified: February 17, 2007