Positive solutions of quasilinear elliptic equations

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...

Large Solutions for Quasilinear Elliptic 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...

Multiple Solutions of Quasilinear Elliptic Equations in RN

On the existence of multiple positive entire solutions for a class of quasilinear elliptic equations

Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in RN with the Schauder-Tychonoff fixed point theorem as the principal tool. In many articles, the theorems of existence and multiple of positive entire solutions for a class semilinear elliptic equations are established. The results of the semilinear equations...