Chen, Zu-Chi; Luo, Tao The eigenvalue problem for the \(p\)-Laplacian-like equations. (English) Zbl 1023.35036 Int. J. Math. Math. Sci. 2003, No. 9, 575-586 (2003). Summary: We consider the eigenvalue problem for the following \(p\)-Laplacian-like equation: \[ -\text{div} (a(|Du|^p)|Du|^{p-2}Du)=\lambda f(x,u) \quad\text{in }\Omega, \qquad u=0\quad\text{on }\partial \Omega, \] where \(\Omega \subset \mathbb{R}^n\) is a bounded smooth domain. When \(\lambda\) is small enough, a multiplicity result for eigenfunctions are obtained. Two examples from nonlinear quantized mechanics and capillary phenomena, respectively, are given for applications of the theorems. Cited in 4 Documents MSC: 35J60 Nonlinear elliptic equations 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs Keywords:multiplicity PDFBibTeX XMLCite \textit{Z.-C. Chen} and \textit{T. Luo}, Int. J. Math. Math. Sci. 2003, No. 9, 575--586 (2003; Zbl 1023.35036) Full Text: DOI EuDML