On existence of solutions for some classes of elliptic problems with supercritical exponential growth

Alves, Claudianor Oliveira; Shen, Liejun

doi:10.1007/s00209-023-03420-5

Math. Z.

2024

DOI: 10.1007/s00209-023-03420-5

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On existence of solutions for some classes of elliptic problems with supercritical exponential growth

Claudianor Oliveira Alves,

Liejun Shen

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2024

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Cited by 2 publications

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“…The local case, that is, the general semilinear elliptic equations (3) with s = 1, has been extensively considered; for example, we shall refer the reader to [20,26,3] and the references therein.…”

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Infinitely many solutions for a class of fractional Schrödinger equations coupled with neutral scalar field

Shen,

Squassina,

Zeng

2024

DCDS-S

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We study the fractional Schrödinger equations coupled with a neutral scalar fieldwhere (−∆) s and (I −∆) t denote the fractional Laplacian and Bessel operators with 3 4 < s < 1 and 0 < t < 1, respectively. Under some suitable assumptions for the external potentials V , K, and g, given q ∈ (1, 2) ∪ (2, 2 * s ) with 2 * s := 6 3−2s , with the help of an improved Fountain theorem dealing with a class of strongly indefinite variational problems approached by Gu-Zhou [Adv. Nonlinear Stud., 17 (2017), 727-738], we show that the system admits infinitely many nontrivial solutions.

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Infinitely many solutions for a class of fractional Schrödinger equations coupled with neutral scalar field

Shen,

Squassina,

Zeng

2024

DCDS-S

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Zero-mass gauged Schrödinger equations with supercritical exponential growth

Shen

2024

Journal of Differential Equations

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On existence of solutions for some classes of elliptic problems with supercritical exponential growth

Cited by 2 publications

References 40 publications

Infinitely many solutions for a class of fractional Schrödinger equations coupled with neutral scalar field

Infinitely many solutions for a class of fractional Schrödinger equations coupled with neutral scalar field

Zero-mass gauged Schrödinger equations with supercritical exponential growth

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