Multiplicity of solutions for a \(p\)-Schrödinger-Kirchhoff-type integro-differential equation (Q2681441)

The authors consider a Schrödinger-Kirchhoff-type integro-differential problem with \(p\)-growth in \(\mathbb{R}^N\), and \(1<p<N<+\infty\), \(N\geq 2\). Nonlocal problems with \(p=2\) have been used to model physical and biological phenomena where the density \(u(x)\) at the point \(x\) is affected by the average of \(u\) on its whole domain. Here, the authors consider a more complicated situation where the nonlinear diffusion process is also governed by the \(p\)-Laplace operator. Under suitable conditions, they prove the existence of a non-trivial ground state solution and, by a Ljusternik-Schnirelman scheme, the existence of infinitely many non-trivial solutions.