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1. Stationary waves of Schrödinger-type equations with variable exponent
Dušan Repovš, 2015, original scientific article

Keywords: Lebesgue-Sobolev spaces with variable exponent, fountain theorem, mountain pass geometry, Leray-Lions operators, hemivariational inequality, resonance
Full text (file, 612,81 KB)

2. 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, 2020, original scientific article

Keywords: 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
Full text (file, 483,22 KB)

3. Multiple solutions of double phase variational problems with variable exponent
Xiayang Shi, Vicenţiu Rǎdulescu, Dušan Repovš, Qihu Zhang, 2020, original scientific article

Keywords: variable exponent elliptic operator, integral functionals, variable exponent Orlicz-Sobolev spaces, critical point
Full text (file, 679,49 KB)

4. The Neumann problem for a class of generalized Kirchhoff-type potential systems
Nabil Chems Eddine, Dušan Repovš, 2023, original scientific article

Keywords: Kirchhoff-type problems, Neumann boundary conditions, p(x)-Laplacian operator, generalized capillary operator, Sobolev spaces with variable exponent, critical Sobolev exponents, concentration–compactness principle, critical point theory, truncation technique
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5. Anisotropic $(p,q)$-equations with convex and negative concave terms
Nikolaos S. Papageorgiou, Dušan Repovš, Calogero Vetro, 2023, independent scientific component part or a chapter in a monograph

Keywords: variable Lebesgue spaces, variable Sobolev spaces, variable ▫$(p,q)$▫-operator, regularity theory, local minimizer, critical point theory
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6. On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
Nabil Chems Eddine, Maria Alessandra Ragusa, Dušan Repovš, 2024, original scientific article

Keywords: Sobolev embeddings, concentration-compactness principle, anisotropic variable exponent Sobolev spaces, p(x)-Laplacian, fractional Brezis-Nirenberg problem
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7. Embeddings of anisotropic Sobolev spaces into spaces of anisotropic Hölder-continuous functions
Nabil Chems Eddine, Dušan Repovš, 2024, original scientific article

Keywords: anisotropic variable exponent Sobolev spaces, critical Sobolev exponent, Sobolev embeddings, anisotropic Hölder-continuous functions, continuous embedding
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