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Existence of Solutions to a Class of Kirchhoff-Type Equation with a General Subcritical Nonlinearity

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Abstract

This paper is devoted to the following nonlinear Kirchhoff-type problem

$$-\bigg(a + b\int_{\Omega}|\nabla u|^{2}\,{d}x\bigg)\Delta u = \lambda f(x,u)$$

with the Dirichlet boundary value. We show that the Kirchhoff-type problem has at least a weak nontrivial solution for all \({\lambda > 0}\) under suitable assumptions on the nonlinear term f with more general growth condition. The main tools are variational method, critical point theory and some analysis techniques.

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Authors and Affiliations

  1. School of Sciences, Jimei University, Xiamen, 361021, People’s Republic of China

    Yong-Yi Lan

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  1. Yong-Yi Lan
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Correspondence to Yong-Yi Lan.

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This work was supported by HuiZhen Huang Foundation for Subject Construction in Jimei University.

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Lan, YY. Existence of Solutions to a Class of Kirchhoff-Type Equation with a General Subcritical Nonlinearity. Mediterr. J. Math. 12, 851–861 (2015). https://doi.org/10.1007/s00009-014-0453-7

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  • DOI: https://doi.org/10.1007/s00009-014-0453-7

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