Description

• Title:
  Solutions to indefinite weakly coupled cooperative elliptic systems
• Creator:
  Clapp, Mónica;
  Szulkin, Andrzej
• Description:
  We study the elliptic system \begin{equation*} \begin{cases} -\Delta u_1 - \kappa_1u_1 = \mu_1|u_1|^{p-2}u_1 + \lambda\alpha|u_1|^{\alpha-2}|u_2|^\beta u_1, \\ -\Delta u_2 - \kappa_2u_2 = \mu_2|u_2|^{p-2}u_2 + \lambda\beta|u_1|^\alpha|u_2|^{\beta-2}u_2, \\ u_1,u_2\in D^{1,2}_0(\Omega), \end{cases} \end{equation*} where $\Omega$ is a bounded domain in $\mathbb R^N$, $N\geq 3$, $\kappa_1,\kappa_2\in\mathbb R$, $\mu_1,\mu_2,\lambda> 0$, $\alpha,\beta> 1$, and $\alpha + \beta = p\le 2^*:={2N}/({N-2})$. For $p\in (2,2^*)$ we establish the existence of a ground state and of a prescribed number of fully nontrivial solutions to this system for $\lambda$ sufficiently large. If $p=2^*$ and $\kappa_1,\kappa_2> 0$ we establish the existence of a ground state for $\lambda$ sufficiently large if, either $N\ge5$, or $N=4$ and neither $\kappa_1$ nor $\kappa_2$ are Dirichlet eigenvalues of $-\Delta$ in $\Omega$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2021.09.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 59, No 2A (June 2022); 553 - 568;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/35206/29658 ;https://apcz.umk.pl/TMNA/article/view/35206/29659
• Subject:
  Weakly coupled elliptic system;
  indefinite;
  cooperative;
  subcritical;
  critical;
  existence and multiplicity of solutions;
  35J57;
  35J50;
  35B33;
  58E30
• Identifier: https://apcz.umk.pl/TMNA/article/view/35206
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other