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

Rafik Guefaifia; Jiabin Zuo; Salah Boulaaras; Praveen Agarwal

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arXiv · 2006.05776

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

Rafik Guefaifia·Jiabin Zuo·Salah Boulaaras·Praveen Agarwal

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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.

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Rafik Guefaifia, Jiabin Zuo, Salah Boulaaras, Praveen Agarwal. 2020-06-10. Existence and multiplicity of positive weak solutions for a new class of $(p; q)$-Laplacian systems. https://arxiv.org/abs/2006.05776

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