Abstract
In this paper, we consider the following elliptic systems with critical Sobolev growth and concave nonlinearities.
where \(B\subset {\mathbb {R}}^{N}\) is an open ball centered at the origin, \(\eta ,\sigma , p, q >0\), \(1<p+q<2\), \(\alpha , \beta >1 \) and \(\alpha +\beta =2^{*}:= \frac{2N}{N-2}\). We establish that if \(N>\frac{2(p+q+1)}{p+q-1}\), the above problem has two distinct and infinite sets of radial solutions. The first set exhibits positive energy, while the second set exhibits negative energy.
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Echarghaoui, R., Sersif, R. Infinitely many solutions for a double critical Sobolev problem with concave nonlinearities. J Elliptic Parabol Equ 9, 1245–1270 (2023). https://doi.org/10.1007/s41808-023-00245-5
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DOI: https://doi.org/10.1007/s41808-023-00245-5