Problem With Critical Sobolev Exponent and With Potential on SN

Problem With Critical Sobolev Exponent and With Potential on SN

We consider the equation in D ’ , u = 0 on D ′ , where D ′ is a geodesic ball with radius θ 1 , centered at the north pole, on , N ≥ 4, and q is a positive continuous function. We prove the existence of solutions that depends only on the behavior of the potential q near its minima.

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Veröffentlicht in:Journal of applied mathematics 2024-01, Vol.2024 (1)
Hauptverfasser: Refai, Walid, Yazidi, Habib
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Lagrange multiplier
Partial differential equations
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Zusammenfassung:We consider the equation in D ’ , u = 0 on D ′ , where D ′ is a geodesic ball with radius θ 1 , centered at the north pole, on , N ≥ 4, and q is a positive continuous function. We prove the existence of solutions that depends only on the behavior of the potential q near its minima.
ISSN:1110-757X
1687-0042
DOI:10.1155/2024/3495135