1. 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: 157; Prenosov: 100 Celotno besedilo (481,56 KB) Gradivo ima več datotek! Več... |
2. 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: 493; Prenosov: 491 Celotno besedilo (550,73 KB) Gradivo ima več datotek! Več... |
3. 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: 300; Prenosov: 166 Celotno besedilo (686,98 KB) Gradivo ima več datotek! Več... |