Existence of solution for a class of nonlocal problem via dynamical methods

In this paper we use the dynamical methods to establish the existence of nontrivial solution for a class of nonlocal problem of the type $$ \left\{\begin{array}{l} -a\left(x,\int_Ωg(u)\,dx \right)Δu =f(u), \quad x \in Ω\\ u=0, \hspace{2 cm} x \in \partial Ω, \end{array}\right. \leqno{(P)} $$ where $Ω\subset \mathbb{R}^N \, ( N \geq 2)$ is a smooth bounded domain and $a:\overlineΩ \times \mathbb{R} \to \mathbb{R}$ and $g,f: \mathbb{R} \to \mathbb{R}$ are $C^1$-functions that satisfy some technical conditions.

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