Infinitely Many Solutions for Semilinear ∆γ-Differential Equations in RN without the Ambrosetti-Rabinowitz Condition
Minimax theory and its applications, Tome 5 (2020) no. 1
We study the existence of infinitely many nontrivial solutions of the semilinear ∆γ-differential equations in RN −∆γu+b(x)u = f(x,u) in RN, where ∆γ is the subelliptic operator of the type N ∆γ := j=1 ∂xj γ2 j∂xj , ∂xj := ∂ ∂xj , γ :=(γ1,γ2,...,γN), and the potential b(x) and nonlinearity f(x,u) are not assumed to be continuous, moreover f may not satisfy the Ambrosetti–Rabinowitz (AR) condition. Under some growth conditions on b and f, we show that there are infinitely many solutions to the problem.
Mots-clés :
∆γ-Laplace problems, Cerami condition, variational method, weak solutions, Moun tain Pass Theorem
@article{MTA_2020_5_1_a1,
author = {Duong Trong Luyen,Le Thi Hong Hanh},
title = {Infinitely {Many} {Solutions} for {Semilinear} {\ensuremath{\Delta}\ensuremath{\gamma}-Differential} {Equations} in {RN} without the {Ambrosetti-Rabinowitz} {Condition}},
journal = {Minimax theory and its applications},
year = {2020},
volume = {5},
number = {1},
url = {http://geodesic.mathdoc.fr/item/MTA_2020_5_1_a1/}
}
TY - JOUR AU - Duong Trong Luyen,Le Thi Hong Hanh TI - Infinitely Many Solutions for Semilinear ∆γ-Differential Equations in RN without the Ambrosetti-Rabinowitz Condition JO - Minimax theory and its applications PY - 2020 VL - 5 IS - 1 UR - http://geodesic.mathdoc.fr/item/MTA_2020_5_1_a1/ ID - MTA_2020_5_1_a1 ER -
%0 Journal Article %A Duong Trong Luyen,Le Thi Hong Hanh %T Infinitely Many Solutions for Semilinear ∆γ-Differential Equations in RN without the Ambrosetti-Rabinowitz Condition %J Minimax theory and its applications %D 2020 %V 5 %N 1 %U http://geodesic.mathdoc.fr/item/MTA_2020_5_1_a1/ %F MTA_2020_5_1_a1
Duong Trong Luyen,Le Thi Hong Hanh. Infinitely Many Solutions for Semilinear ∆γ-Differential Equations in RN without the Ambrosetti-Rabinowitz Condition. Minimax theory and its applications, Tome 5 (2020) no. 1. http://geodesic.mathdoc.fr/item/MTA_2020_5_1_a1/