Multiplicity of nodal solutions for a class of double-phase problems (Q2189643)

Summary: We consider the following parametric double-phase problem: \[\begin{cases} - \operatorname{div} (|\nabla u|^{p - 2} \nabla u + a (x)| \nabla u|^{q - 2} \nabla u) = \lambda f (x,u) &\text{ in } \Omega, \\ u = 0 , &\text{ on } \partial \Omega.\end{cases}\] We do not impose any global growth conditions to the nonlinearity \(f(x,u)\), which refer solely to its behavior in a neighborhood of \(u=0\). And we will show that they suffice for the multiplicity of signed and nodal solutions of the double-phase problem above when \(\lambda\) is large enough.