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Št. zadetkov: 5
On critical variable-order Kirchhoff type problems with variable singular exponent
Jiabin Zuo, Debajyoti Choudhuri, Dušan Repovš
Izvirni znanstveni članek
Oznake: fractional Laplacian of variable-order;continuous embedding;genus;symmetric mountain pass theorem;variable singular exponent;
We establish a continuous embedding ▫$W^{s(\cdot),2}(\Omega) \hookrightarrow L^{\alpha (\cdot)}(\Omega)$▫, where the variable exponent ▫$\alpha(x)$▫ can be close to the critical exponent ▫$2_s^\ast = \frac{2N}{N-2\bar{s}(x)}$▫, with ▫$\bar{s}(x) = s(x,x)$▫ for all ▫$x \in \bar{\Omega}$▫. Subsequentl ...
Leto: 2022 Vir: Fakulteta za matematiko in fiziko (UL FMF)
Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents
Jiabin Zuo, Debajyoti Choudhuri, Dušan Repovš
Izvirni znanstveni članek
Oznake: Choquard type;variable-order fractional operator;mixed operator;variable singular exponent;discontinuous power nonlinearity;
We prove the existence of solutions for the following critical Choquard type problem with a variable-order fractional Laplacian and a variable singular exponent ▫$$\begin{aligned} \begin{aligned} a(-\varDelta )^{s(\cdot )}u+b(-\varDelta )u&=\lambda |u|^{-\gamma (x)-1}u+\left( \int _{\varOmega }\frac ...
Leto: 2022 Vir: Fakulteta za matematiko in fiziko (UL FMF)
On nonlinear biharmonic problems on the Heisenberg group
Jiabin Zuo, Said Taarabti, Tianqing An, Dušan Repovš
Izvirni znanstveni članek
Oznake: Heisenberg group $\mathbb{H}^n$;bi-Kohn Laplacian;Mountain Pass Theorem;variational theory;
We investigate the boundary value problem for biharmonic operators on the Heisenberg group. The inherent features of ▫$\mathbb{H}^n$▫ make it an appropriate environment for studying symmetry rules and the interaction of analysis and geometry with manifolds. The goal of this paper is to prove that a ...
Leto: 2022 Vir: Fakulteta za matematiko in fiziko (UL FMF)
On a fourth-order Neumann problem in variable exponent spaces
Jiabin Zuo, Zakaria El Allali, Said Taarabti, Dušan Repovš
Izvirni znanstveni članek
Oznake: Neumann problem;Leray-Lions operator;Variational methods;Ricceri’s three critical points;Fountain theorem;
We study the Neumann problem with Leray-Lions type operator. Using the classical variational theory, we prove the existence, uniqueness and multiplicity of solutions. As far as we know, this is the first attempt to investigate such a fourth-order problem involving Leray-Lions type operators.
Leto: 2023 Vir: Fakulteta za matematiko in fiziko (UL FMF)
Multiplicity of solutions for a class of fractional p(x, [cdot])-Kirchhoff-type problems without the Ambrosetti-Rabinowitz condition
Mohamed Karim Hamdani, Jiabin Zuo, Nguyen Thanh Chung, Dušan Repovš
Izvirni znanstveni članek
Oznake: fractional ▫$p(x,\cdot)$▫-Kirchhoff-type problems;▫$p(x,\cdot)$▫-fractional Laplace operator;Ambrosetti-Rabinowitz type conditions;symmetric mountain pass theorem;Cerami compactness condition;fractional Sobolev spaces with variable exponent;multiplicity of solutions;
We are interested in the existence of solutions for the following fractional ▫$p(x,\cdot)$▫-Kirchhoff-type problem: ▫$$\textstyle\begin{cases} M ( \int _{\Omega \times \Omega } {\frac{ \vert u(x)-u(y) \vert ^{p(x,y)}}{p(x,y) \vert x-y \vert ^{N+p(x,y)s}}} \,dx \,dy )(-\Delta )^{s}_{p(x,\cdot )}u = f ...
Leto: 2020 Vir: Fakulteta za matematiko in fiziko (UL FMF)
Št. zadetkov: 5
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