Original scientific paper
A remark on the radial solutions of a modified Schrödinger system by the dual approach
Dragos-Patru Covei
; Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, 1st District, Bucharest, Romania
Abstract
By using some reorganized ideas combined with successive approximationtechnique we establish conditions for the existence of positive entireradially symmetric solutions for a modified Schr\"{o}dinger system%\begin{equation*}\left\{ \begin{array}{l}\Delta u_{1}+\Delta (|u_{1}|^{2\gamma _{1}})\left\vert u_{1}\right\vert^{2\gamma _{1}-2}u_{1}=a_{1}(\left\vert x\right\vert )\Psi _{1}\left(u_{1}\right) F_{1}(u_{2})\text{ in }\mathbb{R}^{N}\text{,} \\ \Delta u_{2}+\Delta (|u_{2}|^{2\gamma _{2}})\left\vert u_{2}\right\vert^{2\gamma _{2}-2}u_{2}=a_{2}(\left\vert x\right\vert )\Psi _{2}\left(u_{2}\right) F_{2}(u_{1})\text{ in }\mathbb{R}^{N}\text{,}%\end{array}%\right. \end{equation*}%where $\gamma _{1},\gamma _{2}\in \left( \frac{1}{2},\infty \right) $, $%N\geq 3$ and the functions $a_{1}$, $a_{2}$, $\Psi _{1}\left( u_{1}\right) $%, $\Psi _{2}\left( u_{2}\right) $, $F_{1}$, $F_{2}$ are suitably chosen. Ourobtained results improve and extend some previous works and haveapplications in several areas of mathematics and various applied sciencesincluding the study of nonreactive scattering of atoms and molecules.
Keywords
partial differential equations; cooperative systems; linear systems; nonlinear systems; approximation methods
Hrčak ID:
227104
URI
Publication date:
25.10.2019.
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