Existence of solution for a class of nonlocal problem via dynamical methods

Kirchhoff type elliptic equations with double criticality in Musielak–Sobolev spaces

“…When (x, t) = t p , (1) reduces to a Kirchhoff type problem for p-Laplace operator. Lions 2 setup an abstract framework for the study of such problems and thereafter several authors obtained existence results for p-Kirchhoff type equations, see previous works [3][4][5][6][7][8][9][10][11][12][13][14][15] and references therein. If (x, t) = t p(x) , (1) transforms into a Kirchhoff type problem with variable exponent and existence results are such problems are studied in the variable exponent Sobolev spaces.…”

“…When $$$ \mathcal{H}\left(x,t\right)={t}^p $$$, () reduces to a Kirchhoff type problem for $$$ p $$$‐Laplace operator. Lions 2 setup an abstract framework for the study of such problems and thereafter several authors obtained existence results for $$$ p $$$‐Kirchhoff type equations, see previous works 3–15 and references therein. If $$$ \mathcal{H}\left(x,t\right)={t}^{p(x)} $$$, () transforms into a Kirchhoff type problem with variable exponent and existence results are such problems are studied in the variable exponent Sobolev spaces.…”

On critical exponential Kirchhoff systems on the Heisenberg group

“…Mingqi et al [15] studied the existence and multiplicity of solutions for a class of perturbed fractional Kirchhoff type problems with singular exponential nonlinearity. Alves and Boudjeriou [1] obtained the existence of a nontrivial solution for a class of nonlocal problems by using the dynamical methods. For several interesting results recovering the Kirchhoff-type problems, we refer to Ambrosio et al [3], Caponi and Pucci [6], Mingqi et al [14], and Pucci et al [23], and the references therein.…”

Kirchhoff type elliptic equations with double criticality in Musielak-Sobolev spaces

“…When H(x, t) = t p , (1.1) reduces to a Kirchhoff type problem for p-Laplace operator. Lions [39] set-up an abstract framework for the study of such problems and thereafter several authors obtained existence results for p-Kirchhoff type equations, see [3,4,5,12,25,29,45,47,49,50] and references therein. If H(x, t) = t p(x) , (1.1) transforms into a Kirchhoff type problem with variable exponent and existence results are such problems are studied in the variable exponent Sobolev spaces.…”