Multiple solutions of double phase variational problems with variable exponent
Shi, Xiayang (Avtor), Rǎdulescu, Vicenţiu (Avtor), Repovš, Dušan (Avtor), Zhang, Qihu (Avtor)

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Izvleček
This paper deals with the existence of multiple solutions for the quasilinear equation ▫$$-\text{div} \mathbf{A} (x,\nabla u)+|u|^{\alpha(x)-2}u = f(x,u) \quad \text{in} \; \mathbb{R}^N,$$▫ which involves a general variable exponent elliptic operator ▫$\mathbf{A}$▫ in divergence form. The problem corresponds to double phase anisotropic phenomena, in the sense that the differential operator has various types of behavior like ▫$|\xi|^{q(x)-2} \xi$▫ for small ▫$|\xi|$▫ and like ▫$|\xi|^{p(x)-2} \xi$▫ for large ▫$|\xi|$▫, where ▫$1 < \alpha(\cdot) \le p(\cdot) < q(\cdot) < N$▫. Our aim is to approach variationally the problem by using the tools of critical points theory in generalized Orlicz-Sobolev spaces with variable exponent. Our results extend the previous works [A. Azzollini, P. d'Avenia and A. Pomponio, Quasilinear elliptic equations in ▫$\mathbb{R}^N$▫ via variational methods and Orlicz-Sobolev embeddings, Calc. Var. Partial Differential Equations 49 2014, 1-2, 197-213] and [N. Chorfi and V. D. Rǎdulescu, Standing wave solutions of a quasilinear degenerate Schrödinger equation with unbounded potential, Electron. J. Qual. Theory Differ. Equ. 2016 2016, Paper No. 37] from cases where the exponents ▫$p$▫ and ▫$q$▫ are constant, to the case where ▫$p(\cdot)$▫ and ▫$q(\cdot)$▫ are functions. We also substantially weaken some of the hypotheses in these papers and we overcome the lack of compactness by using the weighting method.

Jezik: Angleški jezik variable exponent elliptic operator, integral functionals, variable exponent Orlicz-Sobolev spaces, critical point Članek v reviji (dk_c) 1.01 - Izvirni znanstveni članek PEF - Pedagoška fakultetaFMF - Fakulteta za matematiko in fiziko 2020 Str. 385-401 Vol. 13, iss. 4 517.956 1864-8258 10.1515/acv-2018-0003 18383193 217 184 (0 glasov) Ocenjevanje je dovoljeno samo prijavljenim uporabnikom. AddThis uporablja piškotke, za katere potrebujemo vaše privoljenje.Uredi privoljenje...

Naslov: Advances in calculus of variations Adv. calc. var. de Gruyter 1864-8258 517905177

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