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Sign-changing solutions for non-local elliptic equations with asymptotically linear term

  • * Corresponding author: XHT

    * Corresponding author: XHT 

XHT is supported by NNSF grant No.11571370

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  • In this article, we study the existence of sign-changing solutions for a problem driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary condition

    $\left\{ \begin{array}{ll}-\mathcal{L}_Ku = f(x,u) &\text{in}~Ω, \\u = 0 &\text{in}~\mathbb{R}^n\setminusΩ, \end{array} \right.\ \ \ \ \ \ \ \ \ \left( 1 \right)$

    where $Ω\subset\mathbb{R}^n(n≥2)$ is a bounded, smooth domain and $f(x, u)$ is asymptotically linear at infinity with respect to $u$. By introducing some new ideas and combining constraint variational method with the quantitative deformation lemma, we prove that there exists a sign-changing solution of problem (1).

    Mathematics Subject Classification: Primary: 35R11; Secondary: 58E30.


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