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In this article, we study the existence of non-negative solutions of the class of non-local problem of n-Kirchhoff type $$\begin{aligned} \left\{ \begin{array}{l} -m(\int _{\Omega }|\nabla u|^n)\Delta _n u = f(x,u) \; \text {in}\; \Omega ,\quad u =0\quad \text {on} \quad \partial \Omega , \end{array} \right. \end{aligned}$$where \(\Omega \subset \mathbb R^n\) is a bounded domain with smooth boundary, \(n\ge 2\) and f behaves like \(e^{|u|^{\frac{n}{n-1}}}\) as \(|u|\rightarrow \infty \). Moreover, by minimization on the suitable subset of the Nehari manifold, we study the existence and multiplicity of solutions, when f(x, t) is concave near \(t=0\) and convex as \(t\rightarrow \infty \). Keywords Kirchhoff equation Trudinger-Moser embedding Sign-changing weight function Mathematics Subject Classification 35J35 35J60 35J92 Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (32) References1.Adimurthi, A.: Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the \(n\)-Laplacian. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17, 393–413 (1990)MathSciNetMATH2.Adimurthi, A., Sandeep, K.: A singular Moser-Trudinger embedding and its applications. Nonlinear Differ. Equ. 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Matemáticas Volume 110, Issue 1 , pp 219-245 Cover Date2016-03 DOI 10.1007/s13398-015-0230-x Print ISSN 1578-7303 Online ISSN 1579-1505 Publisher Springer Milan Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Mathematics, general Applications of Mathematics Theoretical, Mathematical and Computational Physics Keywords Kirchhoff equation Trudinger-Moser embedding Sign-changing weight function 35J35 35J60 35J92 Authors Sarika Goyal (1) Pawan Kumar Mishra (1) K. Sreenadh (1) Author Affiliations 1. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110 016, India Continue reading... To view the rest of this content please follow the download PDF link above.