Positive increasing solutions of quasilinear dynamic equations

Positive decreasing solutions of quasilinear dynamic equations

We consider a quasilinear dynamic equation reducing to a half-linear equation, an Emden–Fowler equation or a Sturm–Liouville equation under some conditions. Any nontrivial solution of the quasilinear dynamic equation is eventually monotone. In other words, it can be either positive decreasing (negative increasing) or positive increasing (negative decreasing). In particular, we investigate the a...

Positive Solutions of Quasilinear Elliptic Equations

(1.2) { −∆pu = λa(x)|u|p−2u, u ∈ D 0 (Ω), has the least eigenvalue λ1 > 0 with a positive eigenfunction e1 and λ1 is the only eigenvalue having this property (cf. Proposition 3.1). This gives us a possibility to study the existence of an unbounded branch of positive solutions bifurcating from (λ1, 0). When Ω is bounded, the result is well-known, we refer to the survey article of Amann [2] and t...

Asymptotic forms of weakly increasing positive solutions of quasilinear ordinary differential equations

Asymptotic forms are determined for positive solutions which are called weakly increasing solutions to quasilinear ordinary differential equations.

Asymptotic Forms of Weakly Increasing Positive Solutions for Quasilinear Ordinary Differential Equations

Asymptotic forms are determined for positive solutions which are called weakly increasing solutions to quasilinear ordinary differential equations.

Multiple Positive Radial Solutions for Quasilinear Equations in Annular Domains