ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS


Authors

G. A. AFROUZI - Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran. M. KHALEGHY MOGHADDAM - Department of Basic Sciences, Faculty of Agriculture Engineering, Sari Agricultural Sciences and Natural Resources University, Sari, Iran.. J. MOHAMMADPOUR - Department of Mathematics, Islamic Azad Univercitiy Ghaemshahr Branch, P.O. Box163, Ghaemshahr, Iran.. M. ZAMENI - Department of Mathematics, Islamic Azad Univercitiy Ghaemshahr Branch, P.O. Box163, Ghaemshahr, Iran..


Abstract

In this paper, we consider the following Neumann boundary value problem \[ \begin{cases} -u''(x) = u^3(x) - \lambda|u(x)|,\quad x \in (0, 1),\\ u'(0) = 0 = u'(1), \end{cases} \] where \(\lambda\in \mathbb{R}\) is parameter. We study the positive and negative solutions of this problem with respect to a parameter \(\rho \) (i.e. \(u(0) = \rho\)) in all \(\mathbb{R}^*\). By using a quadrature method, we obtain our results. Also we provide some details about the solutions that are obtained.


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ISRP Style

G. A. AFROUZI, M. KHALEGHY MOGHADDAM, J. MOHAMMADPOUR, M. ZAMENI, ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS, Journal of Nonlinear Sciences and Applications, 2 (2009), no. 1, 38-45

AMA Style

AFROUZI G. A., MOGHADDAM M. KHALEGHY, MOHAMMADPOUR J., ZAMENI M., ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS. J. Nonlinear Sci. Appl. (2009); 2(1):38-45

Chicago/Turabian Style

AFROUZI, G. A., MOGHADDAM, M. KHALEGHY, MOHAMMADPOUR , J., ZAMENI, M.. " ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS." Journal of Nonlinear Sciences and Applications, 2, no. 1 (2009): 38-45


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