Academic Journal
Integrable solutions of highly discontinuous implicit functional-integral equations
| العنوان: | Integrable solutions of highly discontinuous implicit functional-integral equations |
|---|---|
| المؤلفون: | P. Cubiotti, J. C. Yao |
| المساهمون: | Cubiotti, P., Yao, J. C. |
| بيانات النشر: | Tulipa Opera Scholarum |
| سنة النشر: | 2024 |
| المجموعة: | Università degli Studi di Messina: IRIS |
| مصطلحات موضوعية: | Implicit functional-integral equations, operator inclusions, lower semicontinuous multifunctions, discontinuity, discontinuous selections |
| الوصف: | Let $I$ be a real compact interval. We deal with the problem of the existence of solutions $u\in L^p(I)$ of the implicit functional-integral equation \begin{equation*} f\Big(t,u(t),\int_Ik(t,s)\,u(\varphi(s))\,ds\Big)=0\quad\hbox{for a.e.}\quad t\in I, \end{equation*} where $Y$ is a closed interval, and $f:I\times Y \times {\bf R}\to{\bf R}$, $k:I\times I\to [0,+\infty[$ and $\varphi:I\to I$ are given functions. Such an equation includes, as special cases, many integral equations studied in the literature. We prove an existence result whose main peculiarity is the following: a function $f(t,y,x)$ satisfying our assumptions can be discontinuous, with respect to the third variable, even at all points $x\in{\bf R}$. As regards the function $y\to f(t,y,x)$, we only require that it is continuous, that it changes its sign over $Y$, and that it is not identically zero over any interval. No assumption of monotonicity is made on $f$. Our result extends and improves several results in the literature. Examples and also counter-examples to possible improvements are presented. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | ELETTRONICO |
| اللغة: | English |
| Relation: | volume:1; issue:2; firstpage:75; lastpage:87; numberofpages:13; journal:Optimization Eruditorum; https://hdl.handle.net/11570/3320632 |
| DOI: | 10.69829/oper-024-0102-ta01 |
| الاتاحة: | https://hdl.handle.net/11570/3320632 https://doi.org/10.69829/oper-024-0102-ta01 https://tulipa-os.com/oper/024-0102/ta-01.php |
| رقم الانضمام: | edsbas.A0625B08 |
| قاعدة البيانات: | BASE |
| DOI: | 10.69829/oper-024-0102-ta01 |
|---|