Geodesic
ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS
AFROUZI, G. A.1 ; MOGHADDAM, M. KHALEGHY2 ; MOHAMMADPOUR , J. 3 ; ZAMENI, M.3
1 Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran
2 Department of Basic Sciences, Faculty of Agriculture Engineering, Sari Agricultural Sciences and Natural Resources University, Sari, Iran.
3 Department of Mathematics, Islamic Azad Univercitiy Ghaemshahr Branch, P.O. Box163, Ghaemshahr, Iran.
Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 1, p. 38-45.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.002.01.06
Classification : 34B15, 34B18
Keywords: Positive and negative solutions, Interior critical points, Quadrature method, Neumann boundary condition, Laplacian problem.

AFROUZI, G. A. 1 ; MOGHADDAM, M. KHALEGHY 2 ; MOHAMMADPOUR , J.  3 ; ZAMENI, M. 3

1 Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran
2 Department of Basic Sciences, Faculty of Agriculture Engineering, Sari Agricultural Sciences and Natural Resources University, Sari, Iran.
3 Department of Mathematics, Islamic Azad Univercitiy Ghaemshahr Branch, P.O. Box163, Ghaemshahr, Iran. 
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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 its applications, Tome 2 (2009) no. 1, p. 38-45. doi : 10.22436/jnsa.002.01.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.002.01.06/

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