Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems
Abstract Consider the one-dimensional quasilinear impulsive boundary value problem involving the p-Laplace operator {−(ϕp(u′))′=λω(t)f(u),0<t<1,−Δu|t=tk=μIk(u(tk)),k=1,2,…,n,Δu′|t=tk=0,k=1,2,…,n,u′(0)=0,u(1)=∫01g(t)u(t)dt, $$ \textstyle\begin{cases} -(\phi_{p}(u'))'=\lambda \omega (t...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-11-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1881-7 |
| _version_ | 1818084680364195840 |
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| author | Peige Qin Meiqiang Feng Ping Li |
| author_facet | Peige Qin Meiqiang Feng Ping Li |
| author_sort | Peige Qin |
| collection | DOAJ |
| description | Abstract Consider the one-dimensional quasilinear impulsive boundary value problem involving the p-Laplace operator {−(ϕp(u′))′=λω(t)f(u),0<t<1,−Δu|t=tk=μIk(u(tk)),k=1,2,…,n,Δu′|t=tk=0,k=1,2,…,n,u′(0)=0,u(1)=∫01g(t)u(t)dt, $$ \textstyle\begin{cases} -(\phi_{p}(u'))'=\lambda \omega (t)f(u), \quad 0< t< 1, \\ -\Delta u|_{t=t_{k}}=\mu I_{k}(u(t_{k})), \quad k=1,2,\ldots,n, \\ \Delta u'|_{t=t_{k}}=0, \quad k=1,2,\ldots,n, \\ u'(0)=0, \qquad u(1)=\int_{0}^{1}g(t)u(t)\,dt, \end{cases} $$ where λ,μ>0 $\lambda, \mu >0$ are two positive parameters, ϕp(s) $\phi_{p}(s)$ is the p-Laplace operator, i.e., ϕp(s)=|s|p−2s $\phi_{p}(s)=|s|^{p-2}s$, p>1 $p>1$, ω(t) $\omega (t)$ changes sign on [0,1] $[0,1]$. Several new results are obtained for the above quasilinear indefinite problem. |
| first_indexed | 2024-12-10T19:57:44Z |
| format | Article |
| id | doaj.art-61d2d1f26b294460ac5812491dc116ac |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T19:57:44Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-61d2d1f26b294460ac5812491dc116ac2022-12-22T01:35:36ZengSpringerOpenAdvances in Difference Equations1687-18472018-11-012018111610.1186/s13662-018-1881-7Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problemsPeige Qin0Meiqiang Feng1Ping Li2School of Applied Science, Beijing Information Science & Technology UniversitySchool of Applied Science, Beijing Information Science & Technology UniversitySchool of Applied Science, Beijing Information Science & Technology UniversityAbstract Consider the one-dimensional quasilinear impulsive boundary value problem involving the p-Laplace operator {−(ϕp(u′))′=λω(t)f(u),0<t<1,−Δu|t=tk=μIk(u(tk)),k=1,2,…,n,Δu′|t=tk=0,k=1,2,…,n,u′(0)=0,u(1)=∫01g(t)u(t)dt, $$ \textstyle\begin{cases} -(\phi_{p}(u'))'=\lambda \omega (t)f(u), \quad 0< t< 1, \\ -\Delta u|_{t=t_{k}}=\mu I_{k}(u(t_{k})), \quad k=1,2,\ldots,n, \\ \Delta u'|_{t=t_{k}}=0, \quad k=1,2,\ldots,n, \\ u'(0)=0, \qquad u(1)=\int_{0}^{1}g(t)u(t)\,dt, \end{cases} $$ where λ,μ>0 $\lambda, \mu >0$ are two positive parameters, ϕp(s) $\phi_{p}(s)$ is the p-Laplace operator, i.e., ϕp(s)=|s|p−2s $\phi_{p}(s)=|s|^{p-2}s$, p>1 $p>1$, ω(t) $\omega (t)$ changes sign on [0,1] $[0,1]$. Several new results are obtained for the above quasilinear indefinite problem.http://link.springer.com/article/10.1186/s13662-018-1881-7Multiplicity of positive solutionsIndefinite weight functionp-Laplace operatorQuasilinear impulsive differential equation |
| spellingShingle | Peige Qin Meiqiang Feng Ping Li Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems Advances in Difference Equations Multiplicity of positive solutions Indefinite weight function p-Laplace operator Quasilinear impulsive differential equation |
| title | Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems |
| title_full | Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems |
| title_fullStr | Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems |
| title_full_unstemmed | Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems |
| title_short | Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems |
| title_sort | positive solutions to one dimensional quasilinear impulsive indefinite boundary value problems |
| topic | Multiplicity of positive solutions Indefinite weight function p-Laplace operator Quasilinear impulsive differential equation |
| url | http://link.springer.com/article/10.1186/s13662-018-1881-7 |
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