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July  2008, 7(4): 905-923. doi: 10.3934/cpaa.2008.7.905

On the existence of nodal solutions for singular one-dimensional $\varphi$-Laplacian problem with asymptotic condition

1. 

Department of Mathematics, Pusan National University, Pusan 609-735, South Korea

Received  July 2007 Revised  February 2008 Published  April 2008

We obtain the existence results of nodal solutions for singular one-dimensional $\varphi$-Laplacian problem with asymptotic condition:

$\varphi (u'(t))' + \lambda h(t) f (u(t)) = 0,\ \ $ a.e. $\ t \in (0,1), \qquad\qquad\qquad\qquad\qquad $ $(\Phi_\lambda)$

$u(0) = 0=u(1),$

where $\varphi : \mathbb R \to \mathbb R$ is an odd increasing homeomorphism, $\lambda$ a positive parameter and $h \in L^1(0,1)$ a nonnegative measurable function on $(0,1)$ which may be singular at $t = 0$ and/or $t = 1,$ and $f \in C(\mathbb R, \mathbb R)$ and is odd.

Citation: Inbo Sim. On the existence of nodal solutions for singular one-dimensional $\varphi$-Laplacian problem with asymptotic condition. Communications on Pure & Applied Analysis, 2008, 7 (4) : 905-923. doi: 10.3934/cpaa.2008.7.905
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