Multiple solutions for a class of nonhomogeneous elliptic systems with Dirichlet boundary or Neumann boundary

2024/06/27 by Xiaoli Yu, Xingyong Zhang, Yu, Xiaoli +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2406.19027

Abstract

In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain Ω⊂ℝ^N and N≥ 1. We exploit the method which is based on [6]. This method let us obtain the concrete open interval about the parameter λ. Since the quasilinear term depends on u and ∇ u, it is necessary for our proofs to use the theory of monotone operators and the skill of adding one dimension to space.

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