New linking theorems with applications to critical growth elliptic problems with jumping nonlinearities

Perera, Kanishka; Sportelli, Caterina

doi:10.1016/j.jde.2022.12.035

Cited by 2 publications

(2 citation statements)

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“…In addition, we remark that, in contrast to what occurs in [PS23,MBPSS24] the space dimension plays no role in theorem 1.1 and the reason is that our proof does not require the use of the Talenti function. This means, in particular, that our result is 'strong' enough that it is not needed to distinguish the low dimension case to the other (see e.g.…”

Section: Introductionmentioning

confidence: 76%

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An existence theory for superposition operators of mixed order subject to jumping nonlinearities

Dipierro,

Perera,

Sportelli

et al. 2024

Nonlinearity

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We consider a superposition operator of the form ∫ [ 0 , 1 ] ( − Δ ) s u d μ ( s ) , for a signed measure µ on the interval of fractional exponents [ 0 , 1 ] , joined to a nonlinearity whose term of homogeneity equal to one is ‘jumping’, i.e. it may present different coefficients in front of the negative and positive parts. The signed measure is supposed to possess a positive contribution coming from the higher exponents that overcomes its negative contribution (if any). The problem taken into account is also of ‘critical’ type, though in this case the critical exponent needs to be carefully selected in terms of the signed measure µ. Not only the operator and the nonlinearity considered here are very general, but our results are new even in special cases of interest and include known results as particular subcases. The possibility of considering operators ‘with the wrong sign’ is also a complete novelty in this setting.

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Section: Introductionmentioning

confidence: 76%

“…• If µ := δ 1 , i.e. if A µ reduces to the classical Laplacian, then problem (1.7) has been recently studied in [PS23]. In particular, [PS23, theorem 1.3] provided the existence of a nontrivial solution when N ⩾ 4.…”

Section: Introductionmentioning

confidence: 99%