Existence and multiplicity of positive solutions for a fourth-order \(p\)-Laplace equation
The author studies some existence and multiplicity results on positive solutions to the following one-dimensional fourth-order \(p\)-Laplace equation \(g(u'')''+\lambda a(t) f(u)=0\), \(0<t<1\), with the BV conditions: \(u(0)=u(1)=u''(0)=u''(1)=0\) or \(u(0)=u'(1)=u''(0)=u'''(1)=0\), where \(g(v)=|v|^{p-2}v\), \(p>1\) , \(f(u)\) is nonnegative continuous in \([0,\infty)\) and \(a(t)\) is nonnegative continuous in \((0,1)\) . The techniques used are based on cone compression/extension theorem.
scientific article; zbMATH DE number 1743796