Least-energy nodal solutions of critical Kirchhoff problems with logarithmic nonlinearity
Liang, Sihua ; Rǎdulescu, Vicenţiu, 1958-
In this paper, we are concerned with the existence of least energy sign-changing solutions for the following fractional Kirchhoff problem with logarithmic and critical nonlinearity: ▫$$\begin{cases} ...\left( a+b[u]_{s,p}^p\right) (-\Delta )^s_pu = \lambda |u|^{q-2}u\ln |u|^2 + |u|^{ p_s^{*}-2 }u &{}\quad \text {in } \Omega , \\ u=0 &{}\quad \text {in } {\mathbb {R}}^N{\setminus } \Omega , \end{cases}$$▫ where ▫$N >sp$▫ with ▫$s \in (0, 1)$▫, ▫$p>1$▫, and ▫$$\begin{aligned}{}[u]_{s,p}^p =\iint _{{\mathbb {R}}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy, \end{aligned}$$▫ ▫$p_s^\ast=Np/(N-ps)$▫ is the fractional critical Sobolev exponent, ▫$\Omega \subset {\mathbb {R}}^N$▫ ▫$(N \ge 3)$▫ is a bounded domain with Lipschitz boundary and ▫$\lambda$▫ is a positive parameter. By using constraint variational methods, topological degree theory and quantitative deformation arguments, we prove that the above problem has one least energy sign-changing solution ▫$u_b$▫. Moreover, for any ▫$\lambda > 0$▫, we show that the energy of ub is strictly larger than two times the ground state energy. Finally, we consider ▫$b$▫ as a parameter and study the convergence property of the least energy sign-changing solution as b ▫$\rightarrow 0$▫.
It was not necessary to add the material to the shelf.
Bibliographic material was successfully added on shelf.
Adding bibliographical material on shelf was not successful.
Material is already on the shelf.
Permalink
URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year
Impact factor
Edition
Category
Classification
JCR
SNIP
JCR
SNIP
JCR
SNIP
JCR
SNIP
Select the library membership card:
DRS,
in which the journal is indexed
Database name
Field
Year
Links to authors' personal bibliographies
Links to information on researchers in the SICRIS system
Subject headings in COBISS General List of Subject Headings
Select pickup location
The material from the parent unit is free. If the material is delivered to the pickup location from another unit, the library may charge you for this service.
PDF
