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math.DS2026
An Index Theorem in Relative K-Theory for First-Order Systems
Robert Skiba, Daniel Strzelecki, Nils Waterstraat
Motivated by bifurcation of branches of homoclinic orbits of dynamical systems, we consider families of first-order equations on the real line and introduce a generalisation of pre…
math.AP2026
Note on the multiplicity of solutions for nonlinear scalar field equations with a critical inverse-square potential
Bartosz Bieganowski, Daniel Strzelecki
We are interested in the multiplicity of solutions to the following scalar field equation $$ -Δu - \frac{(N-2)^2}{4|x|^2} u = g(u), \quad \mbox{in } \mathbb{R}^N \setminus \{0\}. $…