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A non-periodic indefinite variational problem in ℝN with critical exponent
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 2 / May 2023
- Published online by Cambridge University Press:
- 26 June 2023, pp. 579-612
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- Article
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We consider the non-linear Schrödinger equation(Pμ)
in
\begin{equation*}\begin{array}{lc}-\Delta u + V(x) u = \mu f(u) + |u|^{2^*-2}u, &\end{array}\end{equation*}
$\mathbb{R}^N$, 
$N\geq3$, where V changes sign and 
$f(s)/s$, s ≠ 0, is bounded, with V non-periodic in x. The existence of a solution is established employing spectral theory, a general linking theorem due to [12] and interaction between translated solutions of the problem at infinity with some qualitative properties of them.
