On the existence of nodal solutions for singular one-dimensional $\varphi$-Laplacian problem with asymptotic condition
Inbo Sim · Communications on Pure & Applied Analysis · 2008
We obtain the existence results of nodal solutions for singularone-dimensional $\varphi$-Laplacian problem with asymptoticcondition:$\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 increasinghomeomorphism, $\lambda$ a positive parameter and $h \in L^1(0,1)$ anonnegative 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 isodd.