scholarly journals A multiplicity result for a (p, q)-Schrödinger–Kirchhoff type equation

2021 ◽  
Author(s):  
Vincenzo Ambrosio ◽  
Teresa Isernia
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Category Theory ◽  
Type Equation ◽  
Multiplicity Result ◽  
Positive Potential ◽  
Subcritical Growth ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Penalization Techniques

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

scholarly journals Nontrivial Solutions for Time Fractional Nonlinear Schrödinger-Kirchhoff Type Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
N. Nyamoradi ◽  
Y. Zhou ◽  
E. Tayyebi ◽  
B. Ahmad ◽  
A. Alsaedi
Keyword(s):  
Variational Methods ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Type Equation ◽  
Nontrivial Solutions ◽  
Nonlinear Schrödinger ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Left And Right

We study the existence of solutions for time fractional Schrödinger-Kirchhoff type equation involving left and right Liouville-Weyl fractional derivatives via variational methods.

A multiplicity result for asymptotically linear Kirchhoff equations

2017 ◽  
Vol 8 (1) ◽  
pp. 267-277 ◽  
Author(s):  
Chao Ji ◽  
Fei Fang ◽  
Binlin Zhang
Keyword(s):  
Variational Methods ◽  
Ground State ◽  
Type Equation ◽  
Ground State Solution ◽  
Mountain Pass ◽  
Multiplicity Result ◽  
Asymptotically Linear ◽  
Type Solution ◽  
Kirchhoff Equations ◽  
Kirchhoff Type

Abstract In this paper, we study the following Kirchhoff type equation: -\bigg{(}1+b\int_{\mathbb{R}^{N}}\lvert\nabla u|^{2}\,dx\biggr{)}\Delta u+u=a(% x)f(u)\quad\text{in }\mathbb{R}^{N},\qquad u\in H^{1}(\mathbb{R}^{N}), where {N\geq 3} , {b>0} and {f(s)} is asymptotically linear at infinity, that is, {f(s)\sim O(s)} as {s\rightarrow+\infty} . By using variational methods, we obtain the existence of a mountain pass type solution and a ground state solution under appropriate assumptions on {a(x)} .

Ground State and Multiple Solutions for Kirchhoff Type Equations With Critical Exponent

2018 ◽  
Vol 61 (2) ◽  
pp. 353-369 ◽  
Author(s):  
Dongdong Qin ◽  
Yubo He ◽  
Xianhua Tang
Keyword(s):  
Variational Methods ◽  
Critical Exponent ◽  
Positive Solutions ◽  
Ground State ◽  
Multiple Solutions ◽  
Type Equation ◽  
Ground State Solution ◽  
Nehari Manifold ◽  
Kirchhoff Type ◽  
The Nehari Manifold

AbstractIn this paper, we consider the following critical Kirchhoff type equation:By using variational methods that are constrained to the Nehari manifold, we prove that the above equation has a ground state solution for the case when 3 < q < 5. The relation between the number of maxima of Q and the number of positive solutions for the problem is also investigated.

scholarly journals The Existence of Nontrivial Solution for a Class of Kirchhoff-Type Equation of General Convolution Nonlinearity without Any Growth Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 163
Author(s):  
Li Zhou ◽  
Chuanxi Zhu
Keyword(s):  
Variational Methods ◽  
Potential Function ◽  
Nontrivial Solution ◽  
Riesz Potential ◽  
Type Equation ◽  
Growth Conditions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

In this paper, we consider the following Kirchhoff-type equation:{u∈H1(RN),−(a+b∫RN|∇u|2dx)Δu+V(x)u=(Iα*F(u))f(u)+λg(u),inRN, where a>0, b≥0, λ>0, α∈(N−2,N), N≥3, V:RN→R is a potential function and Iα is a Riesz potential of order α∈(N−2,N). Under certain assumptions on V(x), f(u) and g(u), we prove that the equation has at least one nontrivial solution by variational methods.

scholarly journals On a class of Kirchhoff problems via local mountain pass

2020 ◽  
pp. 1-43
Author(s):  
Vincenzo Ambrosio ◽  
Dušan Repovš
Keyword(s):  
Continuous Function ◽  
Small Parameter ◽  
Positive Solutions ◽  
Local Minimum ◽  
Mountain Pass ◽  
Multiplicity Result ◽  
Positive Potential ◽  
Subcritical Growth ◽  
Made In

In the present work we study the multiplicity and concentration of positive solutions for the following class of Kirchhoff problems: − ( ε 2 a + ε b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u = f ( u ) + γ u 5 in  R 3 , u ∈ H 1 ( R 3 ) , u > 0 in  R 3 , where ε > 0 is a small parameter, a , b > 0 are constants, γ ∈ { 0 , 1 }, V is a continuous positive potential with a local minimum, and f is a superlinear continuous function with subcritical growth. The main results are obtained through suitable variational and topological arguments. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. Our theorems extend and improve in several directions the studies made in (Adv. Nonlinear Stud. 14 (2014), 483–510; J. Differ. Equ. 252 (2012), 1813–1834; J. Differ. Equ. 253 (2012), 2314–2351).

scholarly journals Multiple solutions for a Kirchhoff-type equation with general nonlinearity

2018 ◽  
Vol 7 (3) ◽  
pp. 293-306 ◽  
Author(s):  
Sheng-Sen Lu
Keyword(s):  
Variational Methods ◽  
Multiple Solutions ◽  
Type Equation ◽  
Existence Results ◽  
Point Of View ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
General Nonlinearity

AbstractThis paper is devoted to the study of the following autonomous Kirchhoff-type equation: -M\biggl{(}\int_{\mathbb{R}^{N}}|\nabla{u}|^{2}\biggr{)}\Delta{u}=f(u),\quad u% \in H^{1}(\mathbb{R}^{N}),where M is a continuous non-degenerate function and {N\geq 2}. Under suitable additional conditions on M and general Berestycki–Lions-type assumptions on the nonlinearity of f, we establish several existence results of multiple solutions by variational methods, which are also naturally interpreted from a non-variational point of view.

Sign in / Sign up

Export Citation Format

Share Document