Ground states for Kirchhoff equations without compact condition

Positive solutions of Schrödinger-Kirchhoff-Poisson system without compact condition

Ground States for Fractional Kirchhoff Equations with Critical Nonlinearity in Low Dimension

We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti-Rabinowitz type condition or monotonicity assumptions.

Existence Results for a p(x)-Kirchhoff-Type Equation without Ambrosetti-Rabinowitz Condition

After the excellent work of Lions [2], problem (2) has received more attention; see [3–10] and references therein. The p(x)-Laplace operator arises from various phenomena, for instance, the image restoration [11], the electro-rheological fluids [12], and the thermoconvective flows of nonNewtonian fluids [13, 14].The study of thep(x)-Laplace operator is based on the theory of the generalized Leb...

Dispersion and Asymptotic Profiles for Kirchhoff Equations

The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained. These formulae are analysed further to obtain the ti...

Uniqueness of Ground States for Pseudo-relativistic Hartree Equations

We prove uniqueness of ground states Q ∈ H1/2(R3) for the pseudo-relativistic Hartree equation,