A characterization of fast decaying solutions for quasilinear and Wolff type systems with singular coefficients
arXiv:1409.0844 · doi:10.1016/j.jmaa.2014.11.062
Abstract
This paper examines the decay properties of positive solutions for a family of fully nonlinear systems of integral equations containing Wolf potentials and Hardy weights. This class of systems includes examples which are closely related to the Euler-Lagrange equations for several classical inequalities such as the Hardy-Sobolev and Hardy-Littlewood-Sobolev inequalities. In particular, a complete characterization of the fast decaying ground states in terms of their integrability is provided in that bounded and fast decaying solutions are shown to be equivalent to the integrable solutions. In generating this characterization, additional properties for the integrable solutions, such as their boundedness and optimal integrability, are also established. Furthermore, analogous decay properties for systems of quasilinear equations of the weighted Lane-Emden type are also obtained.
arXiv comment26 pages
References in corpus (8)
- Qualitative properties of solutions for an integral system related to the Hardy-Sobolev inequality
- Shooting with degree theory: Analysis of some weighted poly-harmonic systems
- A degree theory approach for the shooting method
- Sharp existence criteria for positive solutions of Hardy-Sobolev type systems
- Quasilinear and Hessian type equations with exponential reaction and measure data
- Decay properties of the Hardy-Littlewood-Sobolev systems of the Lane-Emden type
- Shooting Method with Sign-Changing Nonlinearity
- Qualitative properties of positive solutions of quasilinear equations with Hardy terms