Geodesic
A nonexistence result for a class of quasilinear Schrödinger equations with Berestycki-Lions conditions
Filomat, Tome 37 (2023) no. 5, p. 1497

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In this paper, we study the following quasilinear Schrödinger equation −∆u + V(x)u − [∆(1 + u 2) 1/2 ] u 2(1 + u 2) 1/2 = h(u), x ∈ R N , where N ≥ 3, 2 * = 2N N−2 , V(x) is a potential function. Unlike V ∈ C 2 (R N), we only need to assume that V ∈ C 1 (R N). By using a change of variable, we prove the non-existence of ground state solutions with Berestycki-Lions conditions, which contain the superliner case: lim s→+∞ h(s) s = +∞ and asymptotically linear case: lim s→+∞ h(s) s = η. Our results extend and complement the results in related literature.
DOI : 10.2298/FIL2305497H
Classification : 35J10, 35J20
Keywords: quasilinear Schrödinger equation, nonexistence, ground state solutions, Berestycki-Lions conditions 
Yubo He; Jianhua Chen; Quan Gao. A nonexistence result for a class of quasilinear Schrödinger equations with Berestycki-Lions conditions. Filomat, Tome 37 (2023) no. 5, p. 1497 . doi: 10.2298/FIL2305497H
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     author = {Yubo He and Jianhua Chen and Quan Gao},
     title = {A nonexistence result for a class of quasilinear {Schr\"odinger} equations with {Berestycki-Lions} conditions},
     journal = {Filomat},
     pages = {1497 },
     year = {2023},
     volume = {37},
     number = {5},
     doi = {10.2298/FIL2305497H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2305497H/}
}
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