Multiple solutions for N-Kirchhoff type problems with critical exponential growth in RN

2015 ◽  
Vol 117 ◽  
pp. 159-168 ◽  
Author(s):  
Qin Li ◽  
Zuodong Yang
Keyword(s):  
Exponential Growth ◽  
Multiple Solutions ◽  
Kirchhoff Type ◽  
Critical Exponential Growth ◽  
Kirchhoff Type Problems

Fractional Kirchhoff-type problems with exponential growth without the Ambrosetti–Rabinowitz condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ruichang Pei
Keyword(s):  
Exponential Growth ◽  
Polynomial Growth ◽  
Mountain Pass Theorem ◽  
Nontrivial Solutions ◽  
Kirchhoff Type ◽  
Critical Exponential Growth ◽  
Trudinger Inequality ◽  
Fractional Kirchhoff Type Problems ◽  
Kirchhoff Type Problems ◽  
Subcritical Polynomial Growth

Abstract The main aim of this paper is to investigate the existence of nontrivial solutions for a class of fractional Kirchhoff-type problems with right-hand side nonlinearity which is subcritical or critical exponential growth (subcritical polynomial growth) at infinity. However, it need not satisfy the Ambrosetti–Rabinowitz (AR) condition. Some existence results of nontrivial solutions are established via Mountain Pass Theorem combined with the fractional Moser–Trudinger inequality.

Multiplicity results for elliptic Kirchhoff-type problems

2017 ◽  
Vol 6 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Sami Baraket ◽  
Giovanni Molica Bisci
Keyword(s):  
Weak Solutions ◽  
Multiple Solutions ◽  
Fractional Operators ◽  
Type Problem ◽  
Small Perturbations ◽  
Multiplicity Results ◽  
Nonlinear Part ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Kirchhoff Type Problems

AbstractThe aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach combines variational methods with properties of nonlocal fractional operators.

scholarly journals Ground state solutions for a Kirchhoff type elliptic systems involving critical exponential growth nonlinearities

2021 ◽  
Author(s):  
Shengbing Deng ◽  
Tingting Huang
Keyword(s):  
Ground State ◽  
Exponential Growth ◽  
Elliptic Systems ◽  
Ground State Solution ◽  
State Solution ◽  
Ground State Solutions ◽  
Kirchhoff Type ◽  
Critical Exponential Growth ◽  
Growth Nonlinearities

The aim of this paper is to study the ground state solution for a Kirchhoff type elliptic systems without the Ambrosetti-Rabinowitz condition.

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