In this paper we study a quasilinear elliptic system coupled by Schrödinger equation with p-Laplacian operator and Poisson equation. Some scaling transformation ingenious methods are applied to produce the bounded Palais-Smale sequences existence of nontrivial solutions for is obtained mountain pass theorem.

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space W . The system is equipped with a general class of coupled boundary conditions of the form f|∂Ω ∈ Y and ∂f ∂ν ∈ Y⊥, where Y is a closed subspace of L(∂Ω;W ). We discuss well-posedness and further qualitative properties, systema...

in this paper, we study the multiplicity of positive solutions for the laplacian systems with sign-changing weight functions. using the decomposition of the nehari manifold, we prove that an elliptic system has at least two positive solutions.

We introduce and study a system of coupled nonlocal nonlinear Schrödinger equations that interpolates between the mixed, focusing–defocusing Manakov on one hand limiting case intermediate equation other. show this new system, which we call mixed (IMM) admits multi-soliton solutions governed by complexification hyperbolic Calogero–Moser (CM) system. Furthermore, spatially periodic version IMM fo...

Abstract The mathematical P2D model is a system of strongly coupled nonlinear parabolic-elliptic equations that describes the electrodynamics lithium-ion batteries. In this paper, we present numerical analysis finite element-implicit Euler scheme for such model. We obtain error estimates both spatially semidiscrete and fully discrete systems equations, establish existence uniqueness solution.

In this paper, we prove the existence and stability of subsonic flows for steady full Euler-Poisson system in a two dimensional nozzle of finite length when imposing the electric potential difference on non-insulated boundary from a fixed point at the entrance, and prescribing the pressure at the exit of the nozzle. The Euler-Poisson system for subsonic flow is a hyperbolic-elliptic coupled non...