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Mat. Zametki, 2017, Volume 101, Issue 5, paper published in the English version journal (Mi mz11437)  

This article is cited in 3 scientific papers (total in 3 papers)

Papers published in the English version of the journal

Two Nontrivial Solutions of Boundary-Value Problems for Semilinear $\Delta_{\gamma}$-Differential Equations

D. T. Luyen

Department of Mathematics, Hoa Lu University, Ninh Nhat, Ninh Binh city, Vietnam

Abstract: In this paper, we study the existence of multiple solutions for the boundary-value problem
$$ \Delta_{\gamma} u+f(x,u)=0 \quad in \Omega, \qquad u=0 \quadon \partial \Omega, $$
where $\Omega$ is a bounded domain with smooth boundary in $\mathbb{R}^N$ $(N \ge 2)$ and $\Delta_{\gamma}$ is the subelliptic operator of the type
$$ \Delta_\gamma u =\sum\limits_{j=1}^{N}\partial_{x_j} (\gamma_j^2 \partial_{x_j}u ),\qquad \partial_{x_j}u=\frac{\partial u}{\partial x_{j}},\quad \gamma = (\gamma_1, \gamma_2, …, \gamma_N). $$

We use the three critical point theorem.

Keywords: Semilinear degenerate elliptic equations, critical points, two solutions, multiple solutions.


English version:
Mathematical Notes, 2017, 101:5, 815–823

Bibliographic databases:

Received: 02.11.2016
Language:

Citation: D. T. Luyen, “Two Nontrivial Solutions of Boundary-Value Problems for Semilinear <nobr>$\Delta_{\gamma}$</nobr>-Differential Equations”, Math. Notes, 101:5 (2017), 815–823

Citation in format AMSBIB
\Bibitem{Luy17}
\by D.~T.~Luyen
\paper Two Nontrivial Solutions of Boundary-Value Problems for Semilinear <nobr>$\Delta_{\gamma}$</nobr>-Differential Equations
\jour Math. Notes
\yr 2017
\vol 101
\issue 5
\pages 815--823
\mathnet{http://mi.mathnet.ru/mz11437}
\crossref{https://doi.org/10.1134/S0001434617050078}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3669606}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000404236900007}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85021255138}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Cung The Anh, Lee J., Bui Kim My, “On a Class of Hamiltonian Strongly Degenerate Elliptic Systems With Concave and Convex Nonlinearities”, Complex Var. Elliptic Equ.  crossref  isi
    2. A. E. Kogoj, E. Lanconelli, “Linear and semilinear problems involving $\Delta_\lambda$ -Laplacians”, Electron. J. Differ. Equ. Conf., 2018, no. 25, 167–178  mathscinet  zmath  isi
    3. Duong Trong Luyen, Nguyen Minh Tri, “On the Existence of Multiple Solutions to Boundary Value Problems For Semilinear Elliptic Degenerate Operators”, Complex Var. Elliptic Equ., 64:6 (2019), 1050–1066  crossref  mathscinet  zmath  isi  scopus
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