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Boukhsas, A.; Zerouali, A.; Chakrone, O.; Karim, B.

On a positive solutions for \((p, q)\)-Laplacian Steklov problem with two parameters. (English) Zbl 07801869

Bol. Soc. Parana. Mat. (3) 40, Paper No. 81, 19 p. (2022).
Summary: We study the existence and non-existence of positive solutions for \((p, q)\)-Laplacian Steklov problem with two parameters. The main result of our research is the construction of a continuous curve in plane, which becomes a threshold between the existence and non-existence of positive solutions.

MSC:

35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J20 Variational methods for second-order elliptic equations
35J62 Quasilinear elliptic equations
35J70 Degenerate elliptic equations
35P05 General topics in linear spectral theory for PDEs
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs

Keywords:

\((p, q)\)-Laplacian; nonlinear boundary conditions; indefinite weight; mountain pass theorem; global minimizer; super- and sub-solution; modified Picones identity
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