Critical point approaches for doubly eigenvalue discrete boundary value problems driven by ϕc-Laplacian operator

Under appropriate algebraic conditions on the nonlinearity, using variational methods and critical point theory we discuss the existence of one, two and three solutions for nonlinear discrete Dirichlet boundary value problems driven by ϕc-Laplacian operator involving two parameters λ and µ, without imposing the symmetry or oscillating behavior at infinity on the the nonlinearity, which has applications in the dynamic model of combustible gases, the capillarity problem in hydrodynamics, and the flux-limited diffusion phenomenon. Some applications and examples illustrate the obtained results.