Opis

• Tytuł:
  Multiple solutions of degenerate perturbed elliptic problems involving a subcritical Sobolev exponent
• Twórca:
  Cîrstea, Florica Şt.;
  Rădulescu, Vicenţiu D.
• Opis:
  We study the degenerate elliptic equation $$ -\text{\rm div}(a(x)\nabla u)+b(x)u= K(x)\vert u\vert ^{p-2}u+g(x)\quad \text{\rm in } \mathbb R^{N}, $$ where $N\geq 2$ and $2< p< 2^{*}$. We assume that $a\not\equiv 0$ is a continuous, bounded and nonnegative function, while $b$ and $K$ are positive and essentially bounded in $\mathbb R^{N}$. Under some assumptions on $a$, $b$ and $K$, which control the location of zeros of $a$ and the behaviour of $a$, $b$ and $K$ at infinity we prove that if the perturbation $g$ is sufficiently small then the above problem has at least two distinct solutions in an appropriate weighted Sobolev space. The proof relies essentially on the Ekeland Variational Principle [< i> Nonconvex minimization problems< /i> , Bull. Amer. Math. Soc. < b> 1< /b> (1979), 443–473] and on the Mountain Pass Theorem without the Palais-Smale condition, established in Brezis-Nirenberg [< i> Positive solutions of nonlinear elliptic equations involving critical Sobolev exponent< /i> , Comm. Pure Appl. Math. < b> 36< /b> (1983), 437–477], combined with a weighted variant of the Brezis-Lieb Lemma [< i> A relation between pointwise convergence of functions and convergence of functionals< /i> , Proc. Amer. Math. Soc. < b> 88< /b> (1983), 486–490], in order to overcome the lack of compactness.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Data:
  2000.06.01
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 15, No 2 (June 2000); 283 - 300;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2000.021/9988
• Temat i słowa kluczowe:
  Degenerate elliptic problem;
  weighted Sobolev space;
  unbounded domain;
  perturbation;
  multiple solutions;
  35B20;
  35J60;
  58E05;
  58E30
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2000.021
• Dostawca danych:
  Akademicka Platforma Czasopism
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