Singular Quasilinear Schrödinger Equations with Exponential Growth in Dimension Two

Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity

“…Motivated by these physical and mathematical aspects, Equation (1.5) has attracted the attention of numerous researchers, leading to results of existence and multiplicity of solutions. Noteworthy contributions include the works [10,15,22,25] in dimensions N ≥ 3 and [23,24] in the plane. In the later ones, the nonlinearity p(x, u) is continuous and exhibits exponential critical growth in the sense of Trudinger-Moser inequality.…”

“…Therefore, the strategy used to apply the fixed theorem is different from that of [22]. Our intention is to complement the study carried out in [22] and extend the results obtained in [23,24].…”

“…Problems involving (1.5) with critical nonlinearities in dimension N ≥ 3 have been addressed for instance in [10,17,18]. For dimension two, we can cite [23,24], which consider the nonlinearity with exponential critical growth. However, in these works the authors suppose that the nonlinearity is continuous.…”

“…Condition (A8) is inspired by the Trudinger-Moser inequality in the whole space (see Lemma 2.3). Note that the growth (A8) allows f (x, s) to behave as e (s 2 ) α at infinity, which is the exponential critical growth for this class of problems, for more details see [23,24].…”