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Articles

Generalized critical Kirchhoff-type potential systems with Neumann Boundary conditions

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Pages 3958-3988 | Received 06 Jan 2022, Accepted 17 Mar 2022, Published online: 12 Apr 2022
 

Abstract

In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves a general variable exponent elliptic operator with critical growth. Under some suitable conditions on the nonlinearities, we establish existence and multiplicity of solutions for the problem by using the concentration-compactness principle of Lions for variable exponents and the mountain pass theorem without the Palais–Smale condition.

2010 Mathematics Subject Classifications:

Acknowledgements

The second author wish to thank GNAMPA and the RUDN University Strategic Academic Leadership Program.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by GNAMPA [grant number 2020], PRIN 2017 n.2017AYM8XW004 [grant number 2017AYM8XW004] and RUDN University Strategic Academic Leadership Program [grant number 5-100].

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