Singular Quasilinear Schrödinger Equations with Exponential Growth in Dimension Two
In this work, we study the existence of positive solution for the following class of singular quasilinear Schrödinger equations: - div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = f ( u ) | x | a in R 2 , where a ∈ ( 0 , 2 ) , g : R → R + is a continuously differentiable function, V...
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| Veröffentlicht in: | Mediterranean journal of mathematics 2022-06, Vol.19 (3), Article 120 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this work, we study the existence of positive solution for the following class of singular quasilinear Schrödinger equations:
-
div
(
g
2
(
u
)
∇
u
)
+
g
(
u
)
g
′
(
u
)
|
∇
u
|
2
+
V
(
x
)
u
=
f
(
u
)
|
x
|
a
in
R
2
,
where
a
∈
(
0
,
2
)
,
g
:
R
→
R
+
is a continuously differentiable function,
V
(
x
) is a positive potential and the nonlinearity
f
(
u
) can exhibit critical exponential growth. In order to prove our existence result, we combine minimax methods with a singular version of the Trudinger-Moser inequality. |
|---|---|
| ISSN: | 1660-5446 1660-5454 |
| DOI: | 10.1007/s00009-022-02064-9 |