DeBlasi measure of weak noncompactness and Kubiaczyk’s fixed point theorem for the weakly sequentially continuous mappings are the essential tools to prove the main result.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this article, we prove an existence theorem regarding the weak solutions to the hyperbolic-type partial dynamic equation $$z^{\Gamma\Delta}(x,y)=f(x,y,z(x,y))\;\; x\in T_{1},\;\; y\in T_{2}$$ $$z(x,0)=0,\;\; z(0,y)=0$$ in Banach spaces.
📊
Key Findings & Data:For this purpose, by generalizing the definitions and results of Cichoń et.al. we develop weak partial derivatives, double integrability and the mean value results for double integrals on time scales.
💡
Conclusion & Impact:DeBlasi measure of weak noncompactness and Kubiaczyk’s fixed point theorem for the weakly sequentially continuous mappings are the essential tools to prove the main result.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hyperbolic partial dynamic equation · Banach space · measure of weak noncompactness
Abstract
In this article, we prove an existence theorem regarding the weak solutions to the hyperbolic-type partial dynamic equation $$z^{\Gamma\Delta}(x,y)=f(x,y,z(x,y))\;\; x\in T_{1},\;\; y\in T_{2}$$ $$z(x,0)=0,\;\; z(0,y)=0$$ in Banach spaces. For this purpose, by generalizing the definitions and results of Cichoń et.al. we develop weak partial derivatives, double integrability and the mean value results for double integrals on time scales. DeBlasi measure of weak noncompactness and Kubiaczyk’s fixed point theorem for the weakly sequentially continuous mappings are the essential tools to prove the main result.
Yantir, A., Soyoğlu, D. (2015). Weak solutions of a hyperbolic-type partial dynamic equation in Banach spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 44 Issue: 1. https://ajindex.com/articles/1403333