This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).
Despite gains by women in many professional fields, the top level of local government management ranks continues to be populated primarily by man. The percentage of females serving as local government chief administrators has not increased since the 1980s. Little empirical research exists that attempts to uncover the reason for the gender gap. The purpose of this research is to identify some of the obstacles and barriers that affect a woman’s decision to advance her career in local government. Utilizing an online survey, the authors surveyed female chief administrative officers (CAOs), assistant CAOs, assistant to the CAOs, and deputy CAOs in Illinois. The survey results show that barriers such as a male dominated culture and time commitment to work life and family life are preventing females from achieving higher authority. Mentoring proves to be a positive solution to many of the barriers facing women in local government.
AbstractWe consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the (p, q)-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tools combined with suitable truncations and comparison techniques. We prove a bifurcation-type theorem describing in a precise way the dependence of the set of positive solutions on the parameter $$\lambda $$
λ
. Moreover, we produce minimal positive solutions and determine the monotonicity and continuity properties of the minimal positive solution map.
Abstract
Consider an ordered Banach space and
f,g
two self-operators defined on the interior of its positive cone. In this article, we prove that the equation
f(X)=g(X)
has a positive solution, whenever f is strictly
\alpha
-concave g-monotone or strictly
(-\alpha )
-convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.
AbstractIn this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.
A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian