Global bifurcation result for Dirichlet and Neumann \(p\)-biharmonic problem (Q2474189)

Let \(\psi_p(s)=| s| ^{p-2}s\). The paper deals with the \(p\)-biharmonic equation \[ (\psi_p(u''))''=\lambda \psi_p(u)+g(t,u,u',u''),\quad t\in (0, 1), \] with either the Dirichlet boundary conditions \( u(0) = u'(0) = u(1) = u'(1) = 0 \) or with the Neumann boundary conditions \[ u''(0) = (\psi_p(u''(t)))'| _{t = 0} = u''(1) = (\psi_p(u''(t)))'| _{t = 1} =0. \] As a standard consequence, some Rabinowitz-type global bifurcation results for the above problems are proved. Moreover, the existence of solutions for some related problems is proved.