izpis_h1_title_alt

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

.pdfPDF - Predstavitvena datoteka, prenos (679,49 KB)
MD5: 00E916B3C7556C1EDF1A26FD9073FE3D

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
Ključne besede:variable exponent elliptic operator, integral functionals, variable exponent Orlicz-Sobolev spaces, critical point
Vrsta gradiva:Članek v reviji (dk_c)
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:PEF - Pedagoška fakulteta
FMF - Fakulteta za matematiko in fiziko
Leto izida:2020
Št. strani:Str. 385-401
Številčenje:Vol. 13, iss. 4
UDK:517.956
ISSN pri članku:1864-8258
DOI:10.1515/acv-2018-0003 Povezava se odpre v novem oknu
COBISS.SI-ID:18383193 Povezava se odpre v novem oknu
Število ogledov:217
Število prenosov:184
Metapodatki:XML RDF-CHPDL DC-XML DC-RDF
 
Skupna ocena:(0 glasov)
Vaša ocena:Ocenjevanje je dovoljeno samo prijavljenim uporabnikom.
:
Objavi na:AddThis
AddThis uporablja piškotke, za katere potrebujemo vaše privoljenje.
Uredi privoljenje...

Gradivo je del revije

Naslov:Advances in calculus of variations
Skrajšan naslov:Adv. calc. var.
Založnik:de Gruyter
ISSN:1864-8258
COBISS.SI-ID:517905177 Povezava se odpre v novem oknu

Podobna dela

Podobna dela v RUL:
Podobna dela v drugih slovenskih zbirkah:

Komentarji

Dodaj komentar

Za komentiranje se morate prijaviti.

Komentarji (0)
0 - 0 / 0
 
Ni komentarjev!

Nazaj