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  • Noncoercive resonant ▫$(p,2)$▫-equations
    Papageorgiou, Nikolaos, 1958- ; Rǎdulescu, Vicenţiu, 1958-
    We consider a nonlinear Dirichlet problem driven by the sum of ▫$p$▫-Laplacian and a Laplacian (a ▫$(p,2)$▫-equation) which is resonant at ▫$\pm\infty$▫ with respect to the principal eigenvalue ... ▫$\hat{\lambda}_1(p)$▫ of ▫$(-\Delta_p,W^{1,p}_{0}(\Omega))$▫ and resonant at zero with respect to any nonprincipal eigenvalue of ▫$(-\Delta,H^1_0(\Omega))$▫. At ▫$\pm\infty$▫ the resonance occurs from the right of ▫$\hat{\lambda}_1(p)$▫ and so the energy functional of the problem is indefinite. Using critical groups, we show that the problem has at least one nontrivial smooth solution. The result complements the recent work of Papageorgiou and Rǎdulescu (Appl. Math. Optim. 69:393-43, 2014), where resonant ▫$(p,2)$▫-equations were examined with the resonance occurring from the left of ▫$\hat{\lambda}_1(p)$▫ (coercive problem).
    Vir: Applied mathematics and optimization. - ISSN 0095-4616 (Vol. 76, iss. 3, Dec. 2017, str. 621-639)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2017
    Jezik - angleški
    COBISS.SI-ID - 17803865

    Povezava(-e):

    http://dx.doi.org/10.1007/s00245-016-9363-3
    DOI

vir: Applied mathematics and optimization. - ISSN 0095-4616 (Vol. 76, iss. 3, Dec. 2017, str. 621-639)
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