Local and global behavior of solutions of quasilinear equations of Emden-Fowler type

Classification of positive D1,p(RN)-solutions to the critical p

“…By the classification results in [12](see also [1]) it follows that all the regular radial solutions to P * are given by (1.1).…”

“…Once that the radial symmetry of the solutions has been proved in Theorem 3.1, the proof of Theorem 1.1 follows directly by the classification of the radial solutions obtained in [1,12].…”

Self-similar solutions of the p-Laplace heat equation: the fast diffusion case

“…Using the ideas of [Bidaut-Véron 1989], we construct two of them by using the Anderson and Leighton formula [1968].…”

Quasilinear and Hessian equations of Lane–Emden type

“…In particular, (1.3) may have singular solutions [SZ]. The existence problem for (1.5) has been open ([BV2, Problems 1 and 2]; see also [BV1], [BV3], [Gre]) even for the quasilinear equation −∆ p u = u q + f with good data f ∈ L s (Ω), s > 1. Here solutions are generally understood in the renormalized (entropy) sense for quasilinear equations, and viscosity, or the k-convexity sense, for fully nonlinear equations of Hessian type (see [BMMP], [DMOP], [JLM], [TW1]- [TW3], [Ur]).…”

“…Quasilinear problems of Lane-Emden type (1.3)-(1.5) have been studied extensively over the past 15 years. Universal estimates for solutions, Liouvilletype theorems, and analysis of removable singularities are due to Bidaut-Véron, Mitidieri and Pohozaev [BV1]- [BV3], [BVP], [MP], and Serrin and Zou [SZ]. (See also [BiD], [Gre], [Ver], and the literature cited there.)…”