Existence and asymptotic behavior of solutions for fractional p-Laplacian Kirchhoff type problems

Vollständiger Abstract

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In this article we study the fractional $p$-Laplacian Kirchhoff type problem in \(\mathbb{R}^N\), $$ \Big(a+b\int\int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+sp}}\,dx\,dy\Big) (-\Delta)_p^s u+\lambda V(x)|u|^{p-2}u=f(x,u)+g(x,u), $$ where \(s\in(0,1)\), \(2\leq psp\), \(a, b, \lambda >0\) are parameters. Under suitable assumptions on \(V, f\) and \(g\), if \(b\) is sufficiently small and \(\lambda\) is large enough, we show that the existence of at least two different nontrivial solutions by combining the variational methods and the truncation technique. At the same time, we explore the asymptotic behavior of solutions as \(b\to 0\) and \(\lambda\to \infty\). We also obtain the nonexistence of nontrivial solutions when \(a\) is large enough. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/15/abstr.html