Existence and multiplicity of positive weak solutions for a new class of $(p;q)$-Laplacian systems

Abstract

The paper is concerned with the existence of positive weak solutions for a new class of $\left(p,q\right)$-Laplacian elliptic systems in a bounded domain by means of the method of sub-super solutions. Particularly, we do not need any sign conditions for $\gamma \left(0\right),g\left(0\right),f\left(0\right)$ and $h\left(0\right)$. Moreover, a multiplicity result is obtained when $\gamma \left(0\right)=g\left(0\right)=f\left(0\right)=h\left(0\right)=0.$ Finally, we give some examples to verify our main results.