Ma, Li; Su, Ning Existence, multiplicity and stability results for positive solutions of nonlinear \(p\)-Laplacian equations. (English) Zbl 1106.35019 Chin. Ann. Math., Ser. B 25, No. 2, 275-286 (2004). In the present study the authors are mainly interested in the positive solutions of the following boundary value problem of nonlinear \(p\)-Laplacian equations \[ -\Delta_pu=\lambda f(u),\text{ in }\Omega\quad u=0,\text{ on }\partial\Omega,\tag{1} \] where \(\lambda>0\), \(p>1\), \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) and \(f\) is a given nonnegative, nondecreasing function. The author studies both the existence of solution to (1) and extends part of the Crandall-Rabinowitz bifurcation theory to this problem. Moreover, the stability of solutions of the parabolic counterparts of (1) is investigated. Reviewer: Messoud A. Efendiev (Berlin) Cited in 3 Documents MSC: 35J60 Nonlinear elliptic equations 35K55 Nonlinear parabolic equations 35B32 Bifurcations in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 92D25 Population dynamics (general) Keywords:bifurcation PDFBibTeX XMLCite \textit{L. Ma} and \textit{N. Su}, Chin. Ann. Math., Ser. B 25, No. 2, 275--286 (2004; Zbl 1106.35019) Full Text: DOI References: [10] doi:10.1007/978-1-4612-0895-2 · doi:10.1007/978-1-4612-0895-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.