Minimal Positive Solutions to Some Singular Second-Order Differential Equations

Positive Solutions to Singular Second and Third Order Differential Equations for Quantum Fluids

We analyze a quantum trajectory model given by a steady-state hydrodynamic system for quantum fluids with positive constant temperature in bounded domains for arbitrary large data. The momentum equation can be written as a dispersive thirdorder equation for the particle density where viscous effects are incorporated. The phenomena that admit positivity of the solutions are studied. The cases, o...

Positive Solutions to Second Order Singular Differential Equations Involving the One-dimensional M-laplace Operator

We consider a class of second order quasilinear differential equations with singular ninlinearities. Our main purpose is to investigate in detail the asymptotic behavior of their solutions defined on a positive half-line. The set of all possible positive solutions is classified into five types according to their asymptotic behavior near infinity, and sharp conditions are established for the exi...

Multiplicity of positive solutions to second-order singular differential equations with a parameter

*Correspondence: [email protected] 1College of Science, Hohai University, Nanjing, 210098, China 2Department of Mathematics, Hainan University, Haikou, 570228, China Full list of author information is available at the end of the article Abstract We study the existence and multiplicity of positive periodic solutions for second-order nonlinear damped differential equations by combing the analysis ...

Limit Properties of Solutions of Singular Second-Order Differential Equations

We discuss the properties of the differential equation u′′ t a/t u′ t f t, u t , u′ t , a.e. on 0, T , where a ∈ R\{0}, and f satisfies the Lp-Carathéodory conditions on 0, T × R2 for some p > 1. A full description of the asymptotic behavior for t → 0 of functions u satisfying the equation a.e. on 0, T is given. We also describe the structure of boundary conditions which are necessary and suffi...

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations