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Nodal solutions of the \(p\)-Laplacian with sign-changing weight. (English) Zbl 1298.34040

Summary: We are concerned with determining values of \(\gamma\), for which there exist nodal solutions of the boundary value problem \[ (|u'|^{p-2}u')'+\gamma m(t)f(u)=0,\quad t\in(0,1), \]
\[ u(0)=u(1)=0, \] where \(m\in C[0,1]\) is a sign-changing function, \(F:\mathbb R\to\mathbb R\) with \(f(s)s>0\). The proof of our main results is based upon global bifurcation techniques.

MSC:

34B09 Boundary eigenvalue problems for ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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