Constant-sign solutions of $p$-Laplacian type operators on time scales via variational methods
Bull. Korean Math. Soc. 2012 Vol. 49, No. 6, 1131-1145
Printed November 30, 2012
Li Zhang and Weigao Ge
Beijing Union University, Beijing Institute of Technology
Abstract : The purpose of this paper is to use an appropriate variational framework to discuss the boundary value problem with $p$-Laplacian type operators $$ \left\{\begin{array} {llcc} (\alpha(t,x^{\Delta}(t)))^{\Delta}-a(t)\phi_p(x^{\sigma}(t))+f(\sigma(t),x^{\sigma}(t))=0,~~\Delta{\text -\rm a.e.}~t\in I\nonumber\\ x^{\sigma}(0)=0,\nonumber\\\beta_1x^{\sigma}(1)+\beta_2x^{\Delta}(\sigma(1))=0, \end{array}\nonumber \right. $$ where $\beta_1,\beta_2>0$, $I=[0,1]^{k^2}$, $\alpha(\cdot,x(\cdot))$ is an operator of $p$-Laplacian type, $\mathbb{T}$ is a time scale. Some sufficient conditions for the existence of constant-sign solutions are obtained.
Keywords : $p$-Laplacian, time scale, variational, constant-sign
MSC numbers : 34B24, 35A15
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail:   | Powered by INFOrang Co., Ltd