In this paper, we consider the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem [Formula: see text]where [Formula: see text] is a bounded domain in [Formula: see text], [Formula: see text], with a smooth boundary [Formula: see text], [Formula: see text] and [Formula: see text]. By using variational approach and some subtle analytical skills, the existence ...

We study the existence of sign changing solutions to following problem(0.1){Δu+|u|p−1u=0inΩε;u=0on∂Ωε, where p=n+2n−2 is critical Sobolev exponent and Ωε a bounded smooth domain in Rn, n≥3, form Ωε=Ω\B(0,ε). Here Ω containing origin 0 B(0,ε) denotes ball centered at with radius ε>0. construct new type sign-changing high energy problem (0.1), when parameter ε small enough.

We study the existence of positive solutions for a Riemann–Liouville fractional differential equation with sequential derivatives, parameter and sign-changing singular nonlinearity, subject to nonlocal boundary conditions containing varied derivatives general Riemann–Stieltjes integrals. also present associated Green functions some their properties. In proof main results, we apply Guo–Krasnosel...