Existence of multiple solutions for the one-dimensional singular \(p\)-Laplacian equations. (Chinese. English summary) Zbl 1105.34303
Summary: This paper deals with the existence of multiple solutions for the singular \(p\)-Laplacian nonlinear BVP
\[
\bigl(\varphi(u')\bigr)'+a(t)f(u)= 0,\quad u'(0)=u(1)= 0\text{ or }u(0)=u'(t)=0,
\]
with \(\varphi(s)= |s|^{p-2}s\), \(p>1\). Sufficient conditions are established for the existence of multiple solutions of this problem by using the Leggett-Williams fixed-point theorem. The results presented here generalize many known results.
MSC:
34B16 | Singular nonlinear boundary value problems for ordinary differential equations |
34B15 | Nonlinear boundary value problems for ordinary differential equations |