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2019•Boletim da Sociedade Paranaense de MatemáticaOpen access

On a positive solution for $(p,q)$-Laplace equation with Nonlinear

Abdellah Ahmed Zerouali, Belhadj Karim, Omar Chakrone, Abdelmajid Boukhsas

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Abstract

In the presentp aper, we study the existence and non-existence results of a positive solution for the Steklov eigenvalue problem driven by nonhomogeneous operator $(p,q)$-Laplacian with indefinite weights. We also prove that in the case where $\mu>0$ and with $1 0$ there exists an interval of principal eigenvalues for our Steklov eigenvalue problem.

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What this paper is about

In the presentp aper, we study the existence and non-existence results of a positive solution for the Steklov eigenvalue problem driven by nonhomogeneous operator $(p,q)$-Laplacian with indefinite weights. We also prove that in the case where $\mu>0$ and with $1 0$ there exists an interval of principal eigenvalues for our Steklov eigenvalue problem.

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Available abstract

In the presentp aper, we study the existence and non-existence results of a positive solution for the Steklov eigenvalue problem driven by nonhomogeneous operator $(p,q)$-Laplacian with indefinite weights. We also prove that in the case where $\mu>0$ and with $1 0$ there exists an interval of principal eigenvalues for our Steklov eigenvalue problem.

Key concepts: Eigenvalues and eigenvectors, Laplace operator, Mathematics, p-Laplacian, Operator (biology), Nonlinear system, Mathematical analysis, Interval (graph theory)

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