ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS
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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.
Share and Cite
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
Keywords
- Positive and negative solutions
- Interior critical points
- Quadrature method
- Neumann boundary condition
- Laplacian problem.
MSC
References
-
[1]
I. Addou, On the number of solutions for boundary-value problems with jumping nonlinearities, Ph.D. Thesis, Universit´e des Sciences et de la Technologie Houari Boumedienne, Algiers, Algeria (2000)
-
[2]
G. A. Afruzi, M. Khaleghy Moghadaam, Existence and multiplicity results for a class of p-Laplacian problems with Neumann-Robin boundary conditions, Chaos, Solitons & Fractals, 30 (2006), 967–973.
-
[3]
G. A. Afrouzi, M. Khalehghy Moghaddam, Nonnegative solution Curves of Semipositone Problems With Dirichlet Boundary conditions, Nonlinear Analysis, Theory, methods, and Applications, 61 (2005), 485-489.
-
[4]
F. Ammar–Khodja, Une revue et quelques compléments sur la détermination du nombre des solutions de certains problémes elliptiques semi–linéaires, Thése Doctorat 3é Cycle, Université Pierre et Marie Curie,I, Paris V (1983)
-
[5]
V. Anuradha, C. Maya, R. Shivaji, Positive solutions for a class of nonlinear boundary value problems with Neumann–Robin boundary conditions, J. Math. Anal. Appl. , 236 (1999), 94–124.
-
[6]
A. Castro, R. Shivaji, Nonnegative solutions for a class non-positone problems, Proc. Roy. Soc. Edinburgh, Sect. A , 108 (1988), 291–302.
-
[7]
M. Guedda, L. Veron , Bifurcation phenomena associated to the p-Laplacian operator, Trans. Amer. Math. Soc. , 310 (1988), 419–431.
-
[8]
R. A. Khan, N. A. Asif, Positive solutions for a class of singular two point boundary value problems, J. Nonlinear Sci. Appl., 2 (2009), 126–135.
-
[9]
A. R. Miciano, R. Shivaji, Multiple positive solutions for a class of semipositone Neumann two point boundary value problems, J. Math. Anal. Appl. , 178 (1993), 102–115.