Ústav matematiky
Browse
Recent Submissions
Now showing 1 - 5 of 83
- ItemPlanar Choquard equations with critical exponential reaction and Neumann boundary condition(Wiley, 2024-10-26) Rawat, Sushmita; Radulescu, Vicentiu; Sreenadh, KonijetiWe study the existence of positive weak solutions for the following problem: (Formula presented.) where (Formula presented.) is a bounded domain in (Formula presented.) with smooth boundary, (Formula presented.) is a bounded measurable function on (Formula presented.), (Formula presented.) is nonnegative real number, (Formula presented.) is the unit outer normal to (Formula presented.), (Formula presented.), and (Formula presented.). The functions (Formula presented.) and (Formula presented.) have critical exponential growth, while (Formula presented.) and (Formula presented.) are their primitives. The proofs combine the constrained minimization method with energy methods and topological tools.
- ItemOn solvability of a two-dimensional symmetric nonlinear system of difference equations(Springer, 2024-08-27) Stevič, Stevo; Iričanin, Bratislav; Kosmala, Witold; Šmarda, ZdeněkWe show that the system of difference equations (Formula presented.) where $kN, lN_0, l
- ItemMultiplicity of positive solutions for the fractional Schrödinger-Poisson system with critical nonlocal term(World Scientific, 2024-08-28) Dou, Xilin; He, Xiaoming; Radulescu, VicentiuThis paper deals with the following fractional Schrodinger-Poisson system: (-& UDelta;)su + u - K(x)f|u|2s*-3u = f ?(x)|u|q-2u,x & ISIN; Double-struck capital R3,(-& UDelta;)sf = K(x)|u|2s*-1,x & ISIN; Double-struck capital R3 with multiple competing potentials and a critical nonlocal term, where s & ISIN; (0, 1), q & ISIN; (1, 2) or q & ISIN; (4, 2s*), and 2s* = 6 3-2s is the fractional critical exponent. By combining the Nehari manifold analysis and the Ljusternik-Schnirelmann category theory, we establish how the coefficient K of the nonlocal critical nonlinearity affects the number of positive solutions. We propose a new relation between the number of positive solutions and the category of the global maximal set of K.
- ItemConcentration of solutions for non-autonomous double-phase problems with lack of compactness(Springer Nature, 2024-07-20) zhang, Weiqiang; Zuo, Jiabin; Radulescu, VicentiuThe present paper is devoted to the study of the following double-phase equation (Formula presented.) where N2, 1
- ItemInquiry-Based Linear Algebra Teaching and Learning in a Flipped Classroom Framework: A Case Study(Taylor & Francis, 2024-07-17) Fredriksen, Helge; Rebenda, Josef; Rensaa, Ragnhild Johanne; Pettersen, PetterFlipped Classroom (FC) approaches, which utilize video distribution via modern internet platforms, have recently gained interest as a pedagogical framework. Inquiry Based Mathematics Education (IBME) has proven to be a valid form of task design to motivate active learning and enhance classroom interactivity. This article presents a practical combination of introductory videos and inquiry-based class activities adoptable in a basic linear algebra course for stimulating students’ exploration of the underlying mathematics. Teachers’ and students’ work addressed in the article was realized in two case studies in engineering programs in Norway and the Czech Republic. The learning objective was to connect different interpretations of the matrix equation Ax=b, which is often perceived as challenging for engineering students. Feedback from classroom sessions, interviews, and questionnaires encourage further research and inspired us as teachers to closely examine the mathematics behind the task design.