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Matematicheskie Zametki, 2017, Volume 101, Issue 5, paper published in the English version journal
(Mi mzm11437)
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This article is cited in 14 scientific papers (total in 14 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
$$
\Delta_{\gamma} u+f(x,u)=0 \quad \text{in}\ \ \Omega, \qquad
u=0 \quad\text{on}\ \ \partial \Omega,
$$
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
$$
\Delta_\gamma u =\sum\limits_{j=1}^{N}\partial_{x_j} \left(\gamma_j^2 \partial_{x_j}u \right),\qquad
\partial_{x_j}u=\frac{\partial u}{\partial x_{j}},\quad \gamma = (\gamma_1, \gamma_2, \dots, \gamma_N).
$$
We use the three critical point theorem.
Keywords:
Semilinear degenerate elliptic equations, critical points, two solutions, multiple solutions.
Received: 02.11.2016
Citation:
D. T. Luyen, “Two Nontrivial Solutions of Boundary-Value Problems for Semilinear $\Delta_{\gamma}$-Differential Equations”, Math. Notes, 101:5 (2017), 815–823
Linking options:
https://www.mathnet.ru/eng/mzm11437
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