Abstract
This work is concerned with the entire positive solutions for a (p, q)-Laplacian elliptic system of equations with a gradient term. We find the sufficient condition for nonexistence of entire large positive solutions and existence of infinitely many entire solutions, which are large or bounded.
Highlights
Motivated by the results of the above cited papers, we study the nonexistence and existence of positive entire solutions for system ( . ) deeply, and the results of the semilinear systems are extended to the quasilinear ones
We find that the entire large positive solutions fail to exist if f, g are sublinear and a, b have fast decay at infinity, while f, g satisfy some growth conditions at infinity, and a, b are of slow decay or fast decay at infinity, the system has many infinitely entire solutions, which are large or bounded
) has infinitely many positive entire bounded solutions
Summary
We are concerned only with the entire positive solutions of problem ). An entire large (or explosive) solution of problem Obtained the sufficient condition of nonexistence and existence of positive entire solutions. Motivated by the results of the above cited papers, we study the nonexistence and existence of positive entire solutions for system
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