Volume 6, Issue 1
Positive Solutions for Third Order Three-Point Boundary Value Problems with $p$-Laplacian

J. Nonl. Mod. Anal., 6 (2024), pp. 56-70.

Published online: 2024-03

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In this paper, the existence of positive solutions of the following third-order three-point boundary value problem with $p$-Laplacian $$\begin{cases}(\phi_p(u''(t)))'+f(t,u(t))=0, \ t\in(0,1), \\ u(0)=\alpha u(\eta),\ u(1)=\alpha u(\eta), \ u''(0)=0, \end{cases}$$is studied, where $\phi_p(s) = |s|^{p−2} s,$ $p > 1.$ By using the fixed point index method, we establish sufficient conditions for the existence of at least one or at least two positive solutions for the above boundary value problem. The main result is demonstrated by providing an example as an application.

34A08

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@Article{JNMA-6-56, author = {Feng , Xingfang and Feng , Hanying}, title = {Positive Solutions for Third Order Three-Point Boundary Value Problems with $p$-Laplacian}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {1}, pages = {56--70}, abstract = {

In this paper, the existence of positive solutions of the following third-order three-point boundary value problem with $p$-Laplacian $$\begin{cases}(\phi_p(u''(t)))'+f(t,u(t))=0, \ t\in(0,1), \\ u(0)=\alpha u(\eta),\ u(1)=\alpha u(\eta), \ u''(0)=0, \end{cases}$$is studied, where $\phi_p(s) = |s|^{p−2} s,$ $p > 1.$ By using the fixed point index method, we establish sufficient conditions for the existence of at least one or at least two positive solutions for the above boundary value problem. The main result is demonstrated by providing an example as an application.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.56}, url = {http://global-sci.org/intro/article_detail/jnma/22966.html} }
TY - JOUR T1 - Positive Solutions for Third Order Three-Point Boundary Value Problems with $p$-Laplacian AU - Feng , Xingfang AU - Feng , Hanying JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 56 EP - 70 PY - 2024 DA - 2024/03 SN - 6 DO - http://doi.org/10.12150/jnma.2024.56 UR - https://global-sci.org/intro/article_detail/jnma/22966.html KW - Positive solution, three-point boundary value problem, fixed point index, $p$-Laplacian operator. AB -

In this paper, the existence of positive solutions of the following third-order three-point boundary value problem with $p$-Laplacian $$\begin{cases}(\phi_p(u''(t)))'+f(t,u(t))=0, \ t\in(0,1), \\ u(0)=\alpha u(\eta),\ u(1)=\alpha u(\eta), \ u''(0)=0, \end{cases}$$is studied, where $\phi_p(s) = |s|^{p−2} s,$ $p > 1.$ By using the fixed point index method, we establish sufficient conditions for the existence of at least one or at least two positive solutions for the above boundary value problem. The main result is demonstrated by providing an example as an application.

Xingfang Feng & Hanying Feng. (2024). Positive Solutions for Third Order Three-Point Boundary Value Problems with $p$-Laplacian. Journal of Nonlinear Modeling and Analysis. 6 (1). 56-70. doi:10.12150/jnma.2024.56
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