Št. zadetkov: 9
Izvirni znanstveni članek
Oznake:
fractional Laplacian;ground state solution;singularity;
In this paper we establish the existence and multiplicity of nontrivial solutions to the following problem: ▫$$ (-\Delta )^{\frac{1}{2}}u+u+\bigl(\ln \vert \cdot \vert \ast \vert u \vert ^{2}\bigr) = f(u)+\mu \vert u \vert ^{- \gamma -1}u,\quad \text{in }\mathbb{R},$$▫ where ▫$\mu > 0$▫, ▫$(\ast)$▫ ...
Leto:
2021
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
Dirichlet free boundary value problem;stratified Lie group;sub-Laplacian;
In this paper we establish existence of a solution to a semilinear equation with free boundary conditions on stratified Lie groups. In the process, a monotonicity condition is proved, which is quintessential in establishing the regularity of the solution.
Leto:
2023
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
elliptic free boundary problems;mountain pass theorem;singularity;
We establish the existence of at least two solutions of the Prandtl–Batchelor like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable, and hence the usual variational techniques do not work. We shall use a novel approach in tack ...
Leto:
2023
Vir:
Pedagoška fakulteta (UL PEF)
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)
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)
Izvirni znanstveni članek
Oznake:
Choquard term;variational method;dual fountain theorem;singular nonlinearity;
Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded a.e. in the domain ▫$\Omega$▫ and is Hölder continuous.
Leto:
2023
Vir:
Fakulteta za matematiko in fiziko (UL FMF)
Izvirni znanstveni članek
Oznake:
variable exponent Sobolev space;double phase operator;nonlinear boundary condition;Steklov eigenvalue problem;Robin eigenvalue problem;existence;
In this paper we prove the existence of solutions to a double phase problem with a prescribed nonlinear boundary condition which is nonlinear in nature. The driving nonlinear perturbations obey a suitable condition at the origin and on the boundary. To the best of our knowledge, a double phase measu ...
Leto:
2023
Vir:
Pedagoška fakulteta (UL PEF)
Izvirni znanstveni članek
Oznake:
stratified Lie groups;subelliptic operators;Marcinkiewicz space;singular problem;
The article is about an elliptic problem defined on a stratified Lie group. Both sub and superlinear cases are considered whose solutions are guaranteed to exist in light of the interplay between the nonlinearities and the weak ▫$L^1$▫ datum. The existence of infinitely many solutions is proved for ...
Leto:
2025
Vir:
Pedagoška fakulteta (UL PEF)
Izvirni znanstveni članek
Oznake:
multiphase spectral problem;stratified Lie group;Heisenberg group;left invariant vector field;(2,q)-eigenvalue problem;
We consider a multiphase spectral problem on a stratified Lie group.We prove the existence of an eigenfunction of ▫$(2, q)$▫-eigenvalue problem on a bounded domain. Furthermore, we also establish a Pohozaev-like identity corresponding to the problem on the Heisenberg group.
Leto:
2024
Vir:
Repozitorij Univerze v Ljubljani (RUL)