Asymptotic behavior of positive solutions of a nonlinear Dirichlet problem

Asymptotic Behavior of Positive Solutions of a Semilinear Dirichlet Problem outside the Unit Ball

In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundaryvalue problem −∆u = a(x)u in D, lim |x|→1 u(x) = lim |x|→∞ u(x) = 0. Here D is the complement of the closed unit ball of Rn (n ≥ 3), σ < 1 and the function a is a nonnegative function in C loc(D), 0 < γ < 1, satisfying some appropriate assumptions r...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Two positive solutions of a quasilinear elliptic Dirichlet problem

For a class of second order quasilinear elliptic equations we establish the existence of two non-negative weak solutions of the Dirichlet problem on a bounded domain, Ω. Solutions of the boundary value problem are critical points of C−functional on H 0 (Ω). One solution is a local minimum and the other is of mountain pass type. Mathematics Subject Classification (2000). Primary 35J62; Secondary...

Asymptotic Behavior of Positive Solutions of a Class of Systems of Second Order Nonlinear Differential Equations

The two-dimensional system of nonlinear differential equations (A) x′′ = p(t)y, y′′ = q(t)x , with positive exponents α and β satisfying αβ < 1 is analyzed in the framework of regular variation. Under the assumption that p(t) and q(t) are nearly regularly varying it is shown that system (A) may possess three types of positive solutions (x(t), y(t)) which are strongly monotone in the sense that ...