Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 10 2 2025 12 30 Existence and Qualitative Properties of Radial Solutions to a Nonlinear Equation on Lifshitz Black Hole Backgrounds 200 218 2029 10.22128/ansne.2025.3097.1166 EN Sudhaker Upadhyay Department of Physics, K.L.S. College, Nawada, Magadh University, Bodh Gaya, Bihar 805110, India 0000-0002-3880-7315 Journal Article 2025 10 12 We study a nonlinear scalar equation on a $(d{+}2)$--dimensional Lifshitz black hole background with dynamical critical exponent $z>1$.<br />For static, radially symmetric configurations the Klein--Gordon equation with power-type self-interaction reduces to a non-autonomous second-order ordinary differential equation on the half-line. We formulate the problem in divergence form, identify a natural weighted energy, and prove existence of bounded solutions decaying at infinity via a compactness argument and a monotone iteration scheme built upon the positive Green operator of the linearized problem. We also derive sharp near-horizon and asymptotic expansions, and we discuss uniqueness under a smallness condition on the nonlinearity. An explicit family of backgrounds $f(r)=1-(r_h/r)^{d+z}$ is used to illustrate the boundary behavior and to present a numerically robust shooting strategy consistent with the analysis. https://ansne.du.ac.ir/article_2029_b0a651edf3df4e83da674aeac2512f6f.pdf