1. CMB 2015 (vol 59 pp. 73)
 Gasiński, Leszek; Papageorgiou, Nikolaos S.

Positive Solutions for the Generalized Nonlinear Logistic Equations
We consider a nonlinear parametric elliptic equation driven
by a nonhomogeneous differential
operator with a logistic reaction of the superdiffusive type.
Using variational methods coupled with suitable truncation
and comparison techniques,
we prove a bifurcation type result describing the set of positive
solutions
as the parameter varies.
Keywords:positive solution, bifurcation type result, strong comparison principle, nonlinear regularity, nonlinear maximum principle Categories:35J25, 35J92 

2. CMB 2011 (vol 56 pp. 102)
 Kong, Qingkai; Wang, Min

Eigenvalue Approach to Even Order System Periodic Boundary Value Problems
We study an even order system boundary value problem with
periodic boundary conditions. By establishing
the existence of a positive eigenvalue of an associated linear system
SturmLiouville problem, we obtain new conditions for the boundary
value problem to have a positive solution. Our major tools are the
KreinRutman theorem for linear spectra and the fixed point index theory
for compact operators.
Keywords:Green's function, high order system boundary value problems, positive solutions, SturmLiouville problem Categories:34B18, 34B24 

3. CMB 2011 (vol 55 pp. 214)
 Wang, DaBin

Positive Solutions of Impulsive Dynamic System on Time Scales
In this paper, some criteria for the existence of positive solutions of a class
of systems of impulsive dynamic equations on time scales are obtained by
using a fixed point theorem in cones.
Keywords:time scale, positive solution, fixed point, impulsive dynamic equation Categories:39A10, 34B15 

4. CMB 2008 (vol 51 pp. 386)
 Lan, K. Q.; Yang, G. C.

Positive Solutions of the FalknerSkan Equation Arising in the Boundary Layer Theory
The wellknown FalknerSkan equation is one of the most important
equations in laminar boundary layer theory and is used to describe
the steady twodimensional flow of a slightly viscous
incompressible fluid past wedge shaped bodies of angles related to
$\lambda\pi/2$, where $\lambda\in \mathbb R$ is a parameter
involved in the equation. It is known that there exists
$\lambda^{*}<0$ such that the equation with suitable boundary
conditions has at least one positive solution for each $\lambda\ge
\lambda^{*}$ and has no positive solutions for
$\lambda<\lambda^{*}$. The known numerical result shows
$\lambda^{*}=0.1988$. In this paper, $\lambda^{*}\in
[0.4,0.12]$ is proved analytically by establishing a singular
integral equation which is equivalent to the FalknerSkan
equation. The equivalence result
provides new techniques to study properties and existence of solutions of
the FalknerSkan equation.
Keywords:FalknerSkan equation, boundary layer problems, singular integral equation, positive solutions Categories:34B16, 34B18, 34B40, 76D10 

5. CMB 2007 (vol 50 pp. 356)
 Filippakis, Michael E.; Papageorgiou, Nikolaos S.

Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities
In this paper we investigate the existence of positive solutions
for nonlinear elliptic problems driven by the $p$Laplacian with a
nonsmooth potential (hemivariational inequality). Under asymptotic
conditions that make the Euler functional indefinite and
incorporate in our framework the asymptotically linear problems,
using a variational approach based on nonsmooth critical point
theory, we obtain positive smooth solutions. Our analysis also
leads naturally to multiplicity results.
Keywords:$p$Laplacian, locally Lipschitz potential, nonsmooth critical point theory, principal eigenvalue, positive solutions, nonsmooth Mountain Pass Theorem Categories:35J20, 35J60, 35J85 

6. CMB 2001 (vol 44 pp. 210)
 Leung, Man Chun

Growth Estimates on Positive Solutions of the Equation $\Delta u+K u^{\frac{n+2}{n2}}=0$ in $\R^n$
We construct unbounded positive $C^2$solutions of the equation
$\Delta u + K u^{(n + 2)/(n  2)} = 0$ in $\R^n$ (equipped
with Euclidean metric $g_o$) such that $K$ is bounded between two
positive numbers in $\R^n$, the conformal metric $g=u^{4/(n2)}g_o$
is complete, and the volume growth of $g$ can be arbitrarily fast
or reasonably slow according to the constructions. By imposing natural
conditions on $u$, we obtain growth estimate on the $L^{2n/(n2)}$norm
of the solution and show that it has slow decay.
Keywords:positive solution, conformal scalar curvature equation, growth estimate Categories:35J60, 58G03 
