Multiple positive solutions to Kirchhoff equations with competing potential functions in R 3 $\mathbb{R}^{3}$

Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth

In this paper‎, ‎we consider the following Kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$uin H^{1}(mathbb{R}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎The aim of this paper is to study the existence of positive ...

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...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior

Existence and bifurcation of positive solutions to a Kirchhoff type equation ⎧⎪⎨ ⎪⎩ − ( a + b ∫ Ω |∇u|2 ) u= νf (x,u), in Ω, u= 0, on ∂Ω are considered by using topological degree argument and variational method. Here f is a continuous function which is asymptotically linear at zero and is asymptotically 3-linear at infinity. The new results fill in a gap of recent research about the Kirchhoff ...

Existence of positive solutions for a Schrödinger-Poisson system with bounded potential and weighted functions in R3$\mathbb{R}^{3}$

where V (x), a(x) and b(x) are positive and bounded in R, K(x) ∈ L(R) ∪ L∞(R) and K(x) ≥  in R. We will prove the existence of a positive solution (u,φ) ∈ W ,(R) × D,(R) for λ ∈R and  < q <m < ∗, where ∗ =  is the critical exponent for the Sobolev embedding in dimension . The assumption ‘ < q <m < ’ implies that the nonlinear term f (x,u) = a(x)|u|m–u + λb(x)|u|q–u in (.)...