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Existence of positive solutions for a $p$-Laplacian equation with applications to Hematopoiesis | ||
Journal of Mathematical Modeling | ||
دوره 10، شماره 2، شهریور 2022، صفحه 191-201 اصل مقاله (179.37 K) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.22124/jmm.2021.19445.1670 | ||
نویسندگان | ||
Seshadev Padhi1؛ Jaffar Ali2؛ Ankur Kanaujiya3؛ Jugal Mohapatra* 4 | ||
1Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi, India | ||
2Department of Mathematics, Florida Gulf Coast University FortMyres, Florida, USA | ||
3Department of Mathematics, National Institute of Technology Rourkela, India | ||
4Department of Mathematics, National Institute of Technology Rourkela, India | ||
چکیده | ||
This paper is concerned with the existence of at least one positive solution for a boundary value problem (BVP), with $p$-Laplacian, of the form \begin{equation*} \begin{split} (\Phi_p(x^{'}))^{'} + g(t)f(t,x) &= 0, \quad t \in (0,1),\\ x(0)-ax^{'}(0) = \alpha[x], & \quad x(1)+bx^{'}(1) = \beta[x], \end{split} \end{equation*} where $\Phi_{p}(x) = |x|^{p-2}x$ is a one dimensional $p$-Laplacian operator with $p>1, a,b$ are real constants and $\alpha,\beta$ are the Riemann-Stieltjes integrals \begin{equation*} \begin{split} \alpha[x] = \int \limits_{0}^{1} x(t)dA(t), \quad \beta[x] = \int \limits_{0}^{1} x(t)dB(t), \end{split} \end{equation*} with $A$ and $B$ are functions of bounded variation. A Homotopy version of Krasnosel'skii fixed point theorem is used to prove our results. | ||
کلیدواژهها | ||
Fixed point؛ positive solution؛ $p$-Laplacian؛ non-local boundary conditions؛ boundary value problem | ||
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