id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-606	Severo, Uberlandio B.; Ribeiro, Bruno H. C.; Germano, Diogo de S.	Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity	2024	14	.pdf	application/pdf	6050	355	82	Introduction and main result In this work we consider the quasilinear equation − div(g2(u)∇u) + g(u)g′(u)|∇u|2 + V (x)u = f(x, u) + λ|u|p−2u+ h(x)g(u) (1.1) in R2, where g : R → R+ is a function of class C1, V : R2 → R is a potential that can change sign, f : R2 × R → R is a measurable function, which may have exponential critical growth of Trudinger-Moser type, λ ∈ R is a parameter, p ≥ 2 and h ∈ Lq(R2) for some 1 < q ≤ 2. When g(s) ≡ 1 and λ = 0, equation (1.1) becomes the nonhomogeneous semilin- ear Schrödinger equation −∆u+ V (x)u = f(x, u) + h(x) in R2, (1.2) which has been studied by several researchers, see for example	cache/ejde-606.pdf	txt/ejde-606.txt