2 research outputs found
Radial and nonradial solutions for a semilinear elliptic system of Schr\"odinger type
In this article we consider the system of equations
{\Delta}u_{i}=p_{i}(x)f_{i}(u_{1},...,u_{d}) for i=1,...,d on R^{N}, N\geq3 and
d\in{1,2,3,4,...}. We prove that the considered system has a bounded positive
entire solution under some conditions on p_{i} and f_{i}. Also, we give a
necessary condition as well as a sufficient condition for a positive radial
solution to be large. The method of proving theorems is essentially based on a
successive approximation. Furthermore, a non-radially symmetric solution is
obtained by using a lower and upper solution method.Comment: to appear in Funkcialaj Ekvacio
Existence and Non-Existence Criteria for Solutions of a Schr\"odinger Quasilinear System type
In this paper we analyze the existence of large positive radial solutions to
some quasilinear elliptic systems. Also, a non-radially symmetric solution is
obtained by using a lower and upper solution method. The equations are coupled
by functions which are increasing with respect to all the variables.Comment: 12 page