1. On subelliptic equations on stratified Lie groups driven by singular nonlinearity and weak $L^1$ dataSubhashree Sahu, Debajyoti Choudhuri, Dušan Repovš, 2025, izvirni znanstveni članek Povzetek: 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 suitable values of $\lambda$, $p$, $q$ by using the Symmetric Mountain Pass Theorem.
Ključne besede: stratified Lie groups, subelliptic operators, Marcinkiewicz space, singular problem
Objavljeno v DiRROS: 19.08.2025; Ogledov: 290; Prenosov: 169
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2. On the interplay between productively Menger and productively Hurewicz spaces in models of ▫$\mathfrak{b} = \mathfrak{d}$▫Dušan Repovš, Lyubomyr Zdomskyy, 2025, izvirni znanstveni članek Povzetek: This article is devoted to the interplay between productively Menger and productively Hurewicz subspaces of the Cantor space. In particular, we show that in the Laver model for the consistency of the Borel's conjecture these two notions coincide and characterize Hurewicz spaces. On the other hand, it is consistent with CH that there are productively Hurewicz subspaces of the Cantor space which are not productively Menger.
Ključne besede: Menger space, Hurewicz space, Laver forcing, CH, preservation by products
Objavljeno v DiRROS: 15.07.2025; Ogledov: 330; Prenosov: 209
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4. A multiphase eigenvalue problem on a stratified Lie groupDebajyoti Choudhuri, Leandro S. Tavares, Dušan Repovš, 2024, izvirni znanstveni članek Povzetek: 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.
Ključne besede: multiphase spectral problem, stratified Lie group, Heisenberg group, left invariant vector field, (2, q)-eigenvalue problem
Objavljeno v DiRROS: 15.11.2024; Ogledov: 681; Prenosov: 361
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5. Pairs of fixed points for a class of operators on Hilbert spacesAbdelhak Mokhtari, Kamel Saoudi, Dušan Repovš, 2024, izvirni znanstveni članek Povzetek: In this paper, existence of pairs of solutions is obtained for compact potential operators on Hilbert spaces. An application to a second-order boundary value problem is also given as an illustration of our results.
Ključne besede: Hilbert spaces, potential operators, genus, fixed point theorem, boundary value problem
Objavljeno v DiRROS: 26.08.2024; Ogledov: 776; Prenosov: 400
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6. Singular $p$-biharmonic problem with the Hardy potentialAmor Drissi, Abdeljabbar Ghanmi, Dušan Repovš, 2024, izvirni znanstveni članek Povzetek: The aim of this paper is to study existence results for a singular problem involving the $p$-biharmonic operator and the Hardy potential. More precisely, by combining monotonicity arguments with the variational method, the existence of solutions is established. By using the Nehari manifold method, the multiplicity of solutions is proved. An example is also given to illustrate the importance of these results.
Ključne besede: p-biharmonic equation, variational methods, existence of solutions, Hardy potential, Nehari manifold, fibering map
Objavljeno v DiRROS: 08.07.2024; Ogledov: 900; Prenosov: 439
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7. Generalized noncooperative Schrödinger-Kirchhoff-type systems in ${\mathbb R}^N$Nabil Chems Eddine, Dušan Repovš, 2024, izvirni znanstveni članek Povzetek: We consider a class of noncooperative Schrödinger-Kirchhof-type system, which involves a general variable exponent elliptic operator with critical growth. Under certain suitable conditions on the nonlinearities, we establish the existence of infinitely many solutions for the problem by using the limit index theory, a version of concentration-compactness principle for weighted-variable exponent Sobolev spaces and the principle of symmetric criticality of Krawcewicz and Marzantowicz.
Ključne besede: concentration–compactness principle, critical points theory, critical Sobolev exponents, generalized capillary operator, limit index theory, p-Laplacian, p(x)-Laplacian, Palais–Smale condition, Schrödinger-Kirchhoff-type problems, weighted exponent spaces
Objavljeno v DiRROS: 17.06.2024; Ogledov: 850; Prenosov: 555
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8. On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applicationsNabil Chems Eddine, Maria Alessandra Ragusa, Dušan Repovš, 2024, izvirni znanstveni članek Povzetek: We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there is potential for future extensions, particularly in extending the concentration-compactness principle to anisotropic fractional order Sobolev spaces with variable exponents in bounded domains. This extension could find applications in solving the generalized fractional Brezis–Nirenberg problem.
Ključne besede: Sobolev embeddings, concentration-compactness principle, anisotropic variable exponent Sobolev spaces, p(x)-Laplacian, fractional Brezis-Nirenberg problem
Objavljeno v DiRROS: 20.03.2024; Ogledov: 1240; Prenosov: 898
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9. On the Schrödinger-Poisson system with $(p,q)$-LaplacianYueqiang Song, Yuanyuan Huo, Dušan Repovš, 2023, izvirni znanstveni članek Povzetek: We study a class of Schrödinger-Poisson systems with $(p,q)$-Laplacian. Using fixed point theory, we obtain a new existence result for nontrivial solutions. The main novelty of the paper is the combination of a double phase operator and the nonlocal term. Our results generalize some known results.
Ključne besede: double phase operator, Schrödinger-Poisson systems, (p, q)–Laplacian, fixed point theory
Objavljeno v DiRROS: 14.03.2024; Ogledov: 965; Prenosov: 540
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10. Fractional Sobolev spaces with kernel function on compact Riemannian manifoldsAhmed Aberqi, Abdesslam Ouaziz, Dušan Repovš, 2024, izvirni znanstveni članek Povzetek: In this paper, a new class of Sobolev spaces with kernel function satisfying a Lévy-integrability-type condition on compact Riemannian manifolds is presented. We establish the properties of separability, reflexivity, and completeness. An embedding result is also proved. As an application, we prove the existence of solutions for a nonlocal elliptic problem involving the fractional $p(\cdot, \cdot)$-Laplacian operator. As one of the main tools, topological degree theory is applied.
Ključne besede: nonlinear elliptic problem, fractional Sobolev spaces, kernel function, Lévy-integrability condition, compact Riemannian manifolds, existence of solutions, topological degree theory
Objavljeno v DiRROS: 19.02.2024; Ogledov: 1154; Prenosov: 506
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