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JOURNALS // Zapiski Nauchnykh Seminarov POMI

Zap. Nauchn. Sem. POMI, 2021, Volume 508, Pages 124–133 (Mi znsl7172)

New classes of solutions to semilinear equations in $\mathbb R^n$ with fractional Laplacian
A. I. Nazarov, A. P. Shcheglova

References

1. M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Lan, SPb., 2010
2. J. F. Bonder, N. Saintier, A. Silva, “The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem”, Nonlin. Diff. Eq. Appl., 25 (2018), 52  crossref  zmath
3. S. Dipierro, G. Palatucci, E. Valdinoci, “Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian”, Matematiche, 68 (2013), 201–216  zmath
4. L. M. Lerman, P. E. Naryshkin, A. I. Nazarov, “Abundance of entire solutions to nonlinear elliptic equations by the variational method”, Nonlin. Analysis, 190 (2020), 111590  crossref  zmath
5. S. Mosconi, K.Perera, M. Squassina, Y. Yang, “The Brezis-Nirenberg problem for the fractional $p$-Laplacian”, Calc. Var. Part. Differ. Eqs., 55:4 (2016), 105  crossref  zmath
6. R. Musina, A. I. Nazarov, “On the Sobolev and Hardy constants for the fractional Navier Laplacian”, Nonlin. Analysis, 121 (2015), 123–129  crossref  zmath  elib
7. V. G. Osmolovskii, Nelineinaya zadacha Shturma-Liuvillya, Izd-vo SPb. un-ta, SPb., 2003, 230 pp.
8. G. Palatucci, A. Pisante, “Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces”, Calc. Var. Part. Diff. Eqs., 50:3–4 (2014), 799–829  crossref  zmath
9. P. R. Stinga, J. L. Torrea, “Extension problem and Harnack's inequality for some fractional operators”, Comm. Part. Diff. Eqs., 35:11 (2010), 2092–2122  crossref  zmath
10. Kh. Tribel, Teoriya interpolyatsii, funktsionalnye prostranstva, differentsialnye operatory, Mir, M., 1980
11. N. S. Ustinov, “O postoyanstve ekstremali v teoreme vlozheniya drobnogo poryadka”, Funkts. analiz i ego prilozh., 54:4 (2020), 85–97  mathnet  mathscinet  zmath
12. N. S. Ustinov, “O razreshimosti polulineinoi zadachi so spektralnym drobnym laplasianom Neimana i kriticheskoi pravoi chastyu”, Algebra i analiz, 33:1 (2021), 194–212  mathnet  mathscinet


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