Browsing by Subject "positive solution"

Now showing 1 - 8 of 8

Access status: Open Access ,
A note on the dependence of solutions on functional parameters for nonlinear Sturm-Liouville problems
(2014) Orpel, Aleksandra
We deal with the existence and the continuous dependence of solutions on functional parameters for boundary valued problems containing the Sturm-Liouville equation. We apply these result to prove the existence of at least one solution for a certain class of optimal control problems.
Access status: Open Access ,
Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems
(Wydawnictwa AGH, 2022) Zeddini, Noureddine; Sari, Rehab Saeed
Let $D$ be a bounded $C^{1,1}$-domain in $\mathbb{R}^d$, $d \geq 2$. The aim of this article is twofold. The first goal is to give a new characterization of the Kato class of functions $K(D)$ that was defined by N. Zeddini for $d=2$ and by H. Mâagli and M. Zribi for $d \geq 3$ and adapted to study some nonlinear elliptic problems in $D$. The second goal is to prove the existence of positive continuous weak solutions, having the global behavior of the associated homogeneous problem, for sufficiently small values of the nonnegative constants $\lambda$ and $\mu$ to the following system $\Delta u=\lambda f(x,u,v)$, $\Delta v=\mu g(x,u,v)$ in $D$, $u=\phi_{1}$ and $v=\phi_{2}$ on $\partial D$, where $\phi_{1}$ and $\phi_{2}$ are nontrivial nonnegative continuous functions on $\partial D$. The functions $f$ and $g$ are nonnegative and belong to a class of functions containing in particular all functions of the type $f(x,u,v)=p(x)u^{\alpha}h_{1}(v)$ and $g(x,u,v)=q(x)h_{2}(u)v^{\beta} with $\alpha \geq 1$, $\beta \geq 1$, $h_1$, $h_2$ are continuous on $[0,\infty)$ and $p$, $q$ are nonnegative functions in $K(D)$.
Access status: Restricted ,
Istnienie rozwiązań dodatnich dla pewnej klasy problemów brzegowych
(Data obrony: 2009-07-08) Goncerz, Paweł
Wydział Matematyki Stosowanej
Access status: Open Access ,
On a fixed point theorem for operator systems and eigenvalue criteria for existence of positive solutions
(Wydawnictwa AGH, 2026) Fernández-Pardo, Laura M.; Rodríguez-López, Jorge
We provide an alternative approach, based on the Leray-Schauder fixed point index in cones, to a fixed point theorem for operator systems due to Precup. Our focus is on the case of operators whose components are entirely of compressive type. The abstract technique is applied to a system of second-order differential equations providing a coexistence positive solution by means of an eigenvalue type criterion.
Access status: Open Access ,
Positive solutions of arbitrary order nonlinear fractional differential equations with advanced arguments
(2011) Ntouyas, Sotiris K.; Wang, Guotao; Zhang, Lihong
In this paper, we investigate the existence and uniqueness of positive solutions to arbitrary order nonlinear fractional differential equations with advanced arguments. By applying some known fixed point theorems, sufficient conditions for the existence and uniqueness of positive solutions are established.
Access status: Open Access ,
Positive solutions to a third order nonlocal boundary value problem with a parameter
(Wydawnictwa AGH, 2024) Szajnowska, Gabriela; Zima, Mirosława
We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel'skiĭ-Guo fixed point theorem in cones and the properties of the Green's function corresponding to the BVP under study. The main results are illustrated by suitable examples.
Access status: Open Access ,
Right focal boundary value problems for difference equations
(2010) Henderson, Johnny; Liu, Xueyan; Lyons, Jeffrey W.; Neugebauer, Jeffrey T.
An application is made of a new Avery et al. fixed point theorem of compression and expansion functional type in the spirit of the original fixed point work of Leggett and Williams, to obtain positive solutions of the second order right focal discrete boundary value problem. In the application of the fixed point theorem, neither the entire lower nor entire upper boundary is required to be mapped inward or outward. A nontrivial example is also provided.
Access status: Open Access ,
Sobolev norm estimates of solutions for the sublinear Emden-Fowler equation
(2013) Kajikiya, Ryuji
We study the sublinear Emden-Fowler equation in small domains. As the domain becomes smaller, so does any solution. We investigate the convergence rate of the Sobolev norm of solutions as the volume of the domain converges to zero. The result is obtained by estimating the first eigenvalue of the Laplacian with the help of the variational method.