Bifurcation of sign-changing solutions for one-dimensional \(p\)-Laplacian with a strong singular weight: \(p\)-superlinear at \(\infty \)
The authors investigate the one-dimensional \(p\)-Laplacian problem with a weight function \[ \varphi_p(u'(t))+\lambda h(t)f (u(t)) = 0 \text{ a.e. on }(0, 1),\;u(0) = u(1) = 0, \] where \(\varphi_p(s) = |s|^{p-2}s\), \(p>1\), \(\lambda\) is a nonnegative parameter, \(h\) is a nonnegative measurable function on \((0, 1)\), \(h\not\equiv 0\) on any open subinterval in \((0, 1)\) which may be singular at \(t = 0\) and/or \(t = 1\) and \(f\in C(\mathbb{R}, \mathbb{R})\). They obtain the existence, nonexistence, uniqueness and multiplicity of positive solutions as well as sign-changing solutions for the above problems.
scientific article; zbMATH DE number 5959647
scientific article