Existence of solutions for higher order $\phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions
In this paper, we consider the following $(n+1)$st order bvp on the half line with a $\phi-$Laplacian operator $$ \begin{cases} (\phi(u^{(n)}))'(t)=f(t,u(t),\ldots,u^{(n)}(t)),& a.e., \,t\in [ 0,+\infty ),\\& n\in \mathbb{N}\setminus\{0\}, \\ u^{(i)}(0)=A_{i},\, i=0,\ldots,n-2...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universidad de La Frontera
2023-08-01
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| Series: | Cubo |
| Subjects: | |
| Online Access: | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3419/2297 |
| _version_ | 1797676883604668416 |
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| author | A. Zerki K. Bachouche K. Ait-Mahiout |
| author_facet | A. Zerki K. Bachouche K. Ait-Mahiout |
| author_sort | A. Zerki |
| collection | DOAJ |
| description | In this paper, we consider the following $(n+1)$st order bvp on the half line with a $\phi-$Laplacian operator
$$
\begin{cases}
(\phi(u^{(n)}))'(t)=f(t,u(t),\ldots,u^{(n)}(t)),& a.e., \,t\in [ 0,+\infty ),\\& n\in \mathbb{N}\setminus\{0\}, \\
u^{(i)}(0)=A_{i},\, i=0,\ldots,n-2,\\
u^{(n-1)}(0)+au^{(n)}(0)=B,\\
u^{(n)}(+\infty )=C.
\end{cases}
$$
The existence of solutions is obtained by applying Schaefer's fixed point theorem under a one-sided Nagumo condition with nonordered lower and upper solutions method where $f$ is a $L^{1}$-Carath\'eodory function. |
| first_indexed | 2024-03-11T22:36:53Z |
| format | Article |
| id | doaj.art-6b47d1ca871c4a92b0af68175d65942a |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-03-11T22:36:53Z |
| publishDate | 2023-08-01 |
| publisher | Universidad de La Frontera |
| record_format | Article |
| series | Cubo |
| spelling | doaj.art-6b47d1ca871c4a92b0af68175d65942a2023-09-22T13:27:37ZengUniversidad de La FronteraCubo0716-77760719-06462023-08-0125217319310.56754/0719-0646.2502.173Existence of solutions for higher order $\phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutionsA. Zerki0https://orcid.org/0000-0002-2057-3370K. Bachouche1https://orcid.org/0000-0002-4619-9698K. Ait-Mahiout2https://orcid.org/0000-0002-5991-0442Laboratoire “Théorie du point fixe et Applications”, École Normale Supérieure, BP 92, Kouba, 16006, Algiers, Algeria.Departement of Mathematics, Faculty of Sciences, Algiers University 1, Algiers, Algeria and Laboratory of Mathematical Analysis and Applications, Algiers, Algeria.Laboratoire “Théorie du point fixe et Applications”, École Normale Supérieure, BP 92, Kouba, 16006, Algiers, Algeria.In this paper, we consider the following $(n+1)$st order bvp on the half line with a $\phi-$Laplacian operator $$ \begin{cases} (\phi(u^{(n)}))'(t)=f(t,u(t),\ldots,u^{(n)}(t)),& a.e., \,t\in [ 0,+\infty ),\\& n\in \mathbb{N}\setminus\{0\}, \\ u^{(i)}(0)=A_{i},\, i=0,\ldots,n-2,\\ u^{(n-1)}(0)+au^{(n)}(0)=B,\\ u^{(n)}(+\infty )=C. \end{cases} $$ The existence of solutions is obtained by applying Schaefer's fixed point theorem under a one-sided Nagumo condition with nonordered lower and upper solutions method where $f$ is a $L^{1}$-Carath\'eodory function.https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3419/2297boundary value problemone-sided nagumo conditionlower and upper solutionsa priori estimates |
| spellingShingle | A. Zerki K. Bachouche K. Ait-Mahiout Existence of solutions for higher order $\phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions Cubo boundary value problem one-sided nagumo condition lower and upper solutions a priori estimates |
| title | Existence of solutions for higher order $\phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions |
| title_full | Existence of solutions for higher order $\phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions |
| title_fullStr | Existence of solutions for higher order $\phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions |
| title_full_unstemmed | Existence of solutions for higher order $\phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions |
| title_short | Existence of solutions for higher order $\phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions |
| title_sort | existence of solutions for higher order phi laplacian bvps on the half line using a one sided nagumo condition with nonordered upper and lower solutions |
| topic | boundary value problem one-sided nagumo condition lower and upper solutions a priori estimates |
| url | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3419/2297 |
| work_keys_str_mv | AT azerki existenceofsolutionsforhigherorderphilaplacianbvpsonthehalflineusingaonesidednagumoconditionwithnonorderedupperandlowersolutions AT kbachouche existenceofsolutionsforhigherorderphilaplacianbvpsonthehalflineusingaonesidednagumoconditionwithnonorderedupperandlowersolutions AT kaitmahiout existenceofsolutionsforhigherorderphilaplacianbvpsonthehalflineusingaonesidednagumoconditionwithnonorderedupperandlowersolutions |