The Multiplicity of Positive Solutions to A Quasilinear Equation Generated By The Il′in–Caffarelli–Cohn–Nirenberg Inequality

Аннотация

The Euler–Lagrange equation for the functional related to the V. P. Il’in inequality also known as the Caffarelli–Kohn–Nirenberg inequality is considered. We prove that if the space dimension is even, then changing some parameters, one can obtain arbitrary many different positive solutions for this equation.