Existence and topological structure of solution sets for phi-Laplacian impulsive differential equations
In this article, we present results on the existence and the topological structure of the solution set for initial-value problems for the first-order impulsive differential equation $$displaylines{ (phi(y'))' = f(t,y(t)), quadhbox{a.e. } tin [0,b],cr y(t^+_{k})-y(t^-_k)=I_{k}(y(t_{k}^...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2012-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/56/abstr.html |
| _version_ | 1818084824665030656 |
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| author | Johnny Henderson Abdelghani Ouahab Samia Youcefi |
| author_facet | Johnny Henderson Abdelghani Ouahab Samia Youcefi |
| author_sort | Johnny Henderson |
| collection | DOAJ |
| description | In this article, we present results on the existence and the topological structure of the solution set for initial-value problems for the first-order impulsive differential equation $$displaylines{ (phi(y'))' = f(t,y(t)), quadhbox{a.e. } tin [0,b],cr y(t^+_{k})-y(t^-_k)=I_{k}(y(t_{k}^{-})), quad k=1,dots,m,cr y'(t^+_{k})-y'(t^-_k)=ar I_{k}(y'(t_{k}^{-})), quad k=1,dots,m,cr y(0)=A,quad y'(0)=B, }$$ where $0=t_0<t_1<dots<t_m<t_{m+1}=b$, $minmathbb{N}$. The functions $I_k, ar I_k$ characterize the jump in the solutions at impulse points $t_k$, $k=1,dots,m$. For the final result of the paper, the hypotheses are modified so that the nonlinearity $f$ depends on $y'$, but the impulsive conditions and initial conditions remain the same. |
| first_indexed | 2024-12-10T20:00:02Z |
| format | Article |
| id | doaj.art-735cfa2862d946709176700b96fc1152 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T20:00:02Z |
| publishDate | 2012-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-735cfa2862d946709176700b96fc11522022-12-22T01:35:32ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-04-01201256,116Existence and topological structure of solution sets for phi-Laplacian impulsive differential equationsJohnny HendersonAbdelghani OuahabSamia YoucefiIn this article, we present results on the existence and the topological structure of the solution set for initial-value problems for the first-order impulsive differential equation $$displaylines{ (phi(y'))' = f(t,y(t)), quadhbox{a.e. } tin [0,b],cr y(t^+_{k})-y(t^-_k)=I_{k}(y(t_{k}^{-})), quad k=1,dots,m,cr y'(t^+_{k})-y'(t^-_k)=ar I_{k}(y'(t_{k}^{-})), quad k=1,dots,m,cr y(0)=A,quad y'(0)=B, }$$ where $0=t_0<t_1<dots<t_m<t_{m+1}=b$, $minmathbb{N}$. The functions $I_k, ar I_k$ characterize the jump in the solutions at impulse points $t_k$, $k=1,dots,m$. For the final result of the paper, the hypotheses are modified so that the nonlinearity $f$ depends on $y'$, but the impulsive conditions and initial conditions remain the same.http://ejde.math.txstate.edu/Volumes/2012/56/abstr.htmlphi-Laplacianfixed point theoremsimpulsive solutioncompactness |
| spellingShingle | Johnny Henderson Abdelghani Ouahab Samia Youcefi Existence and topological structure of solution sets for phi-Laplacian impulsive differential equations Electronic Journal of Differential Equations phi-Laplacian fixed point theorems impulsive solution compactness |
| title | Existence and topological structure of solution sets for phi-Laplacian impulsive differential equations |
| title_full | Existence and topological structure of solution sets for phi-Laplacian impulsive differential equations |
| title_fullStr | Existence and topological structure of solution sets for phi-Laplacian impulsive differential equations |
| title_full_unstemmed | Existence and topological structure of solution sets for phi-Laplacian impulsive differential equations |
| title_short | Existence and topological structure of solution sets for phi-Laplacian impulsive differential equations |
| title_sort | existence and topological structure of solution sets for phi laplacian impulsive differential equations |
| topic | phi-Laplacian fixed point theorems impulsive solution compactness |
| url | http://ejde.math.txstate.edu/Volumes/2012/56/abstr.html |
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