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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