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 $1<q<p<\infty$ the results are completely different from those for the usua lSteklov eigenvalue problem involving the $p$-Laplacian with indefinite weight, which is retrieved when $\mu=0$. Precisely, we show that when $\mu>0$ there exists an interval of principal eigenvalues for our Steklov eigenvalue problem.
@article{36661,
title = {On a positive solution for $(p,q)$-Laplace equation with Nonlinear},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {38},
year = {2019},
doi = {10.5269/bspm.v38i4.36661},
language = {EN},
url = {http://dml.mathdoc.fr/item/36661}
}
Zerouali, Abdellah; Karim, Belhadj; Chakrone, Omar; Boukhsas, Abdelmajid. On a positive solution for $(p,q)$-Laplace equation with Nonlinear. Boletim da Sociedade Paranaense de Matemática, Tome 38 (2019) . doi : 10.5269/bspm.v38i4.36661. http://gdmltest.u-ga.fr/item/36661/