# IJPAM: Volume 5, No. 3 (2003)

**SOLUTIONS OF SOME ANISOTROPIC EQUATIONS**

Institute of Mathematics

Universitetsparken 5

2100, Copenhagen, DENMARK

e-mail: tad@math.ku.dk

**Abstract.**For the problem (Qc) below, in [#!cite!#]7 we established the following results:

**Theorem A.** *If there are two functions and , which are (Qc)-compatible in with all their second derivatives positive, then:
*

*i) any classical solution of (Qc) satisfies
in . Such a solution is unique if the depend only on ;
*

*ii) if it exists, the solution of (Qc), which has all its second derivatives
positive is unique.*

**Theorem B.** *Under the hypotheses (h1) - (h5),
1) If there are two functions and , which are (Qc)-compatible in
with all their second derivatives positive, then:
*

*i) if the are independent of , (Qc) has a unique solution
such that
in ;
*

*ii) the same conclusion holds when the depend also on but
the uniqueness holds only for solutions, whose all second derivatives are all
positive.*

The object of this note is to complete the work with some extension to the large solutions (as in (Q)).

**Received: **January 10, 2003

**AMS Subject Classification: **35J60, 34B15

**Key Words and Phrases: **(Qc)-compatible, existence and uniqness of solution, partial differential equations

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2003

**Volume:** 5

**Issue:** 3