Browsing by Subject "nonlinear"

Now showing 1 - 3 of 3

Access status: Open Access ,
Existence theorems of nonlinear asymptotic BVP for a homeomorphism
(2016) Szymańska-Dębowska, Katarzyna
In this work, we are concerned with the existence of solutions for the following $\varphi$-Laplacian boundary value problem on the half-line $(\varphi (x'))' =f(t,x,x'),\quad x(0)=0,\quad x'(\infty)=0,$ where $f:\mathbb{R}_+\times\mathbb{R}^k\times\mathbb{R}^k\to\mathbb{R}^k$ is continuous. The results are proved using the properties of the Leray-Schauder topological degree.
Access status: Open Access ,
Oscillation theorems concerning non-linear differential equations of the second order
(2011) Elabbasy, Elmetwally M.; Elzeiny, Sh. R.
This paper concerns the oscillation of solutions of the differential eq. $\left[ r\left( t\right) \psi \left(x\left( t\right) \right) f\text{ }( \overset{\cdot }{x}(t))\right]^{\cdot }+q\left( t\right) \varphi (g\left( x\left( t\right) \right), r\left( t\right) \psi \left( x\left( t\right) \right) f(\overset{\cdot }{x}(t)))=0,$ where $u\varphi \left( u,v\right) \gt 0$ for all $u\neq 0$, $xg\left( x\right) \gt 0$, $xf\left( x\right)\gt 0$ for all $x\neq 0$, $\psi \left( x\right) \gt 0$ for all $x\in \mathbb{R}$, $r\left( t\right) \gt 0$ for $t\geq t_{0}\gt 0$ and $q$ is of arbitrary sign. Our results complement the results in [A.G. Kartsatos, On oscillation of nonlinear equations of second order, J. Math. Anal. Appl. 24 (1968), 665–668], and improve a number of existing oscillation criteria. Our main results are illustrated with examples.
Access status: Open Access ,
Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences
(2006) Schmeidel, Ewa
In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.