Rigorous Numerical Enclosures for Positive Solutions of Lane–Emden’s Equation with Sub-Square Exponents
Rigorous Numerical Enclosures for Positive Solutions of Lane–Emden’s Equation with Sub-Square Exponents
The purpose of this paper is to obtain rigorous numerical enclosures for solutions of Lane–Emden’s equation −Δu=|u|p−1u with homogeneous Dirichlet boundary conditions. We prove the existence of a nondegenerate solution u nearby a numerically computed approximation û together with an explicit error bound, i.e., a bound for the difference between …