Physics

Nonlinear system

Operator (biology)

Pure mathematics

Mountain pass theorem

Mathematics

Boundary (topology)

Transcription factor

Biology

Gene

Critical exponent

Mathematical analysis

Boundary value problem

Artificial intelligence

Multiplicity (mathematics)

Repressor

Neumann boundary condition

Variable (mathematics)

Chemistry

Ecology

Class (philosophy)

Geometry

Type (biology)

Computer science

Quantum mechanics

Biochemistry

Scaling

Applicable Analysis

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.

Generalized critical Kirchhoff-type potential systems with Neumann Boundary conditions