1 results
A Berestycki–Lions type result for a class of degenerate elliptic problems involving the Grushin operator
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 4 / August 2023
- Published online by Cambridge University Press:
- 05 July 2022, pp. 1244-1271
- Print publication:
- August 2023
-
- Article
-
- You have access
- HTML
- Export citation
-
In this work we study the existence of nontrivial solution for the following class of semilinear degenerate elliptic equations
\[ -\Delta_{\gamma} u + a(z)u = f(u) \quad \mbox{in}\ \mathbb{R}^{N}, \]where $\Delta _{\gamma }$
is known as the Grushin operator, $z:=(x,y)\in \mathbb {R}^{m}\times \mathbb {R}^{k}$
and $m+k=N\geqslant 3$
, $f$
and $a$
are continuous function satisfying some technical conditions. In order to overcome some difficulties involving this type of operator, we have proved some compactness results that are crucial in the proof of our main results. For the case $a=1$
, we have showed a Berestycki–Lions type result.
