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- W4313304700 abstract "It is considered a semilinear elliptic partial differential equation in $mathbb{R}^N$ with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the interplay between the decay of the potential at infinity and the behavior of the nonlinear term at the origin. The proof is based on a penalization argument, variational methods, and $L^infty$ estimates. Those estimates allow dealing with settings where the nonlinear source may have supercritical, critical, or subcritical behavior near the origin. Results that provide the existence of multiple and infinitely many solutions when the nonlinear term is odd are also established." @default.
- W4313304700 created "2023-01-06" @default.
- W4313304700 creator A5015477247 @default.
- W4313304700 creator A5029177560 @default.
- W4313304700 date "2022-12-26" @default.
- W4313304700 modified "2023-09-23" @default.
- W4313304700 title "Semilinear elliptic problems in $mathbb{R}^N$: the interplay between the potential and the nonlinear term" @default.
- W4313304700 doi "https://doi.org/10.48550/arxiv.2212.13300" @default.
- W4313304700 hasPublicationYear "2022" @default.
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