Results 61 to 70 of about 2,887 (118)

Existence and multiplicity of solutions for fourth-order elliptic equations of Kirchhoff type via genus theory

, 2014
In this paper, we study the following fourth-order elliptic equations of Kirchhoff type: △2u−(a+b∫R3|∇u|2dx)△u+V(x)u=f(x,u), in R3, u∈H2(R3), where a,b>0 are constants, we have the potential V(x):R3→R and the nonlinearity f(x,u):R3×R→R.
Liping Xu, Haibo Chen
semanticscholar   +1 more source

Symmetry minimizes the principal eigenvalue: an example for the Pucci's sup operator

, 2013
We explicitly evaluate the principal eigenvalue of the extremal Pucci's sup--operator for a class of special plane domains, and we prove that, for fixed area, the eigenvalue is minimal for the most symmetric set.Comment: 11 pages, 7 ...
Birindelli, Isabeau, Leoni, Fabiana
core   +1 more source

Elliptic problems with nonmonotone discontinuities at resonance (Erratum)

, 2004
Abstract and Applied Analysis, Volume 2004, Issue 3, Page 269-270, 2004.
Halidias Nikolaos
wiley   +1 more source

Ground state solution of a noncooperative elliptic system

, 2013
In this paper, we study the existence of a ground state solution, that is, a non trivial solution with least energy, of a noncooperative semilinear elliptic system on a bounded domain.
Batkam, Cyril Joel
core   +1 more source

Inequalities for Green's operator applied to the minimizers

Journal of Inequalities and Applications, 2011
In this paper, we prove both the local and global Lφ -norm inequalities for Green's operator applied to minimizers for functionals defined on differential forms in Lφ -averaging domains.
Ding Shusen, Agarwal Ravi
doaj  

Positive solution for a nonlocal problem with strong singular nonlinearity

Open Mathematics, 2023
In this article, we consider a nonlocal problem with a strong singular term and a general weight function. By using Ekeland’s variational principle, we prove a necessary and sufficient condition for the existence of a positive solution.
Wang Yue, Wei Wei, Xiong Zong-Hong, Yang Jian   +3 more
doaj   +1 more source

Nontrivial solution for Klein-Gordon equation coupled with Born-Infeld theory with critical growth

Advances in Nonlinear Analysis, 2023
In this article, we study the following system: −Δu+V(x)u−(2ω+ϕ)ϕu=λf(u)+∣u∣4u,inR3,Δϕ+βΔ4ϕ=4π(ω+ϕ)u2,inR3,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-\left(2\omega +\phi )\phi u=\lambda f\left(u)+| u{| }^{4}u,& \hspace{0.1em}\text{in}\hspace{0.1em ...
He Chuan-Min, Li Lin, Chen Shang-Jie
doaj   +1 more source

Multiple solutions for weighted Kirchhoff equations involving critical Hardy-Sobolev exponent

Advances in Nonlinear Analysis, 2020
In this article, we consider a class of Kirchhoff equations with critical Hardy-Sobolev exponent and indefinite nonlinearity, which has not been studied in the literature. We prove very nicely that this equation has at least two solutions in ℝ3. And some
Shen Zupei, Yu Jianshe
doaj   +1 more source

Normalized solutions for the p-Laplacian equation with a trapping potential

Advances in Nonlinear Analysis, 2023
In this article, we are concerned with normalized solutions for the pp -Laplacian equation with a trapping potential and Lr{L}^{r}-supercritical growth, where r=pr=p or 2.2.
Wang Chao, Sun Juntao
doaj   +1 more source

Regularity of minimizers for double phase functionals of borderline case with variable exponents

Advances in Nonlinear Analysis
The aim of this article is to study regularity properties of a local minimizer of a double phase functional of type ℱ(u)≔∫Ω(∣Du∣p(x)+a(x)∣Du∣p(x)log(e+∣Du∣))dx,{\mathcal{ {\mathcal F} }}\left(u):= \mathop{\int }\limits_{\Omega }({| Du| }^{p\left(x)}+a ...
Ragusa Maria Alessandra, Tachikawa Atsushi   +1 more
doaj   +1 more source