IJPAM: Volume 5, No. 3 (2003)
Institute of Mathematics
2100, Copenhagen, DENMARK
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