Abstract This paper is dedicated to studying the following Kirchhoff-type problem: $$ \textstyle\begin{cases} -m ( \Vert \nabla u ^{2}_{L^{2}(\mathbb{R} ^{N})} )\Delta u+V(x)u=f(u), &amp; x\in \mathbb{R} ^{N}; \\ u\in H^{1}(\mathbb{R} ^{N}), \end{cases} { ? <mm...

We consider a diffusion problem on a network on whose nodes we impose Dirichlet and generalized, non-local Kirchhoff-type conditions. We prove well-posedness of the associated initial value problem, and we exploit the theory of sub-Markovian and ultracontractive semigroups in order to obtain upper Gaussian estimates for the integral kernel. We conclude that the same diffusion problem is governe...

Abstract In this paper, we study a class of ( p , q )-Schrödinger–Kirchhoff type equations involving continuous positive potential satisfying del Pino–Felmer conditions and nonlinearity with subcritical growth at infinity. By applying variational methods, penalization techniques Lusternik–Schnirelman category theory, relate the number solutions topology set where attains its minimum values.