Multiple Solutions for Ellipticpx,qx-Kirchhoff-Type Potential Systems in Unbounded Domains

Multiple Sign-changing Solutions for Kirchhoff Type Problems

This article concerns the existence of sign-changing solutions to nonlocal Kirchhoff type problems of the form

On the optimality of the observability inequalities for Kirchhoff plate systems with potentials in unbounded domains∗

In this paper, we derive a sharp observability inequality for Kirchhoff plate equations with lower order terms in an unbounded domain Ω of lR. More precisely, when the observation is assumed to be located in a subdomain ω such that Ω \ ω is bounded and the observation time T > 0 is sufficiently large, we establish an observability estimate with an explicit observability constant for Kirchhoff p...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Pullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

Multiple Positive Solutions for Kirchhoff Type Problems Involving Concave and Convex Nonlinearities in R

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theor...