Electron. J. Diff. Equ., Vol. 2014 (2014), No. 151, pp. 1-9.

Existence of solutions to p-Laplacian equations involving general subcritical growth

Yong-Yi Lan

In this article, we consider the quasilinear elliptic equation $-\Delta_p u=\mu f(x,u)$ with the Dirichlet boundary coditions, and under suitable growth condition on the nonlinear term f. Existence of solutions is given for all $\mu>0$ via the variational method and some analysis techniques.

Submitted February 13, 2014. Published June 27, 2014.
Math Subject Classifications: 35B33, 35J92, 35J35.
Key Words: p-Laplacian equation; subcritical growth; variational methods; (C) condition; mountain-pass lemma.

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Yong-Yi Lan
School of Sciences, Jimei University
Xiamen 361021, China
email: lanyongyi@jmu.edu.cn

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