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  • The behavior of solutions of a parametric weighted ▫$(p,q)$▫-Laplacian equation [Elektronski vir]
    Repovš, Dušan, 1954- ; Vetro, Calogero
    We study the behavior of solutions for the parametric equation ▫$$-\Delta_{p}^{a_1} u(z)-\Delta_{q}^{a_2} u(z) = \lambda |u(z)|^{q-2} u(z)+f(z,u(z)) \quad \mbox{in } \Omega,\, \lambda >0,$$▫ under ... Dirichlet condition, where ▫$\Omega \subseteq \mathbb{R}^N$▫ is a bounded domain with a ▫$C^2$▫-boundary ▫$\partial \Omega$▫, ▫$a_1, a_2 \in L^\infty(\Omega)$▫ with ▫$a_1(z), a_2(z) > 0$▫ for a.a. ▫$z \in \Omega$▫, ▫$p, q \in (1, \infty)$▫ and ▫$\Delta_{p}^{a_1}$▫, ▫$\Delta_{q}^{a_2}$▫ are weighted versions of ▫$p$▫-Laplacian and ▫$q$▫-Laplacian. We prove existence and nonexistence of nontrivial solutions, when ▫$f(z,x)$▫ asymptotically as ▫$x \to \pm \infty$▫ can be resonant. In the studied cases, we adopt a variational approach and use truncation and comparison techniques. When ▫$\lambda$▫ is large, we establish the existence of at least three nontrivial smooth solutions with sign information and ordered. Moreover, the critical parameter value is determined in terms of the spectrum of one of the differential operators.
    Vir: AIMS mathematics [Elektronski vir]. - ISSN 2473-6988 (Vol. 7, iss. 1, 2022, str. 499-517)
    Vrsta gradiva - e-članek
    Leto - 2022
    Jezik - angleški
    COBISS.SI-ID - 81064195

    Povezava(-e):

    https://www.aimspress.com/article/doi/10.3934/math.2022032
    Repozitorij Univerze v Ljubljani – RUL
    DOI

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