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

Xiaoli Yu; Xingyong Zhang

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arXiv · 2406.19027

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

Xiaoli Yu·Xingyong Zhang

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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 $\Omega\subset\mathbb{R}^N $ and $N\geq 1$. We exploit the method which is based on [6]. This method let us obtain the concrete open interval about the parameter $\lambda$. Since the quasilinear term depends on $u$ and $\nabla u$, 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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Xiaoli Yu, Xingyong Zhang. 2024-06-27. Multiple solutions for a class of nonhomogeneous elliptic systems with Dirichlet boundary or Neumann boundary. https://arxiv.org/abs/2406.19027

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