Existence of positive solutions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi></mml:math>th-order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math>-Laplacian singular super-linear boundary value problems

The present study focusses on the existence of positivity of the solutions to the higher order three-point boundary value problems involving $p$-Laplacian $$[\phi_{p}(x^{(m)}(t))]^{(n)}=g(t,x(t)),~~t \in [0, 1],$$ $$ \begin{aligned} x^{(i)}(0)=0, &\text{~for~} 0\leq i\leq m-2,\\ x^{(m-2)}(1)&-\alpha x^{(m-2)}(\xi)=0,\\ [\phi_{p}(x^{(m)}(t))]^{(j)}_{\text {at} ~ t=0}&=0, \text{~for~} 0\leq j\leq n-2,\\ [\phi_{p}(x^{(m)}(t))]^{(n-2)}_{\text {at} ~ t=1}&-\alpha[\phi_{p}(x^{(m)}(t))]^{(n-2)}_{\text {at} ~ t=\xi}=0, \end{aligned} $$ where $m,n\geq 3$, $\xi\in(0,1)$, $\alpha\in (0,\frac{1}{\xi})$ is a parameter. The approach used by the application of Guo--Krasnosel'skii fixed point theorem to determine the existence of positivity of the solutions to the problem.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Existence of positive solutions fornth-orderp-Laplacian singular super-linear boundary value problems

Cited by 2 publications

References 13 publications

Existence of Positive Solutions for Higher Order p-Laplacian Boundary Value Problems

Existence of Positive Solutions for Higher Order p-Laplacian Boundary Value Problems

Existence of Positivity of the Solutions for Higher Order Three-Point Boundary Value Problems involving p-Laplacian

Contact Info

Product

Resources

About