We classify finite Morse index solutions of the following nonlocal Lane-Emden equation (−∆)u = |u|p−1u R for 1 < s < 2 via a novel monotonicity formula. For local cases s = 1 and s = 2 this classification is provided by Farina in [10] and Davila, Dupaigne, Wang and Wei in [8], respectively. Moreover, for the nonlocal case 0 < s < 1 finite Morse index solutions are classified by Davila, Dupaigne...

We prove that positive solutions of the superlinear Lane–Emden system in a two-dimensional smooth bounded domain are independently exponents system, provided comparable. As consequence, energy is uniformly bounded, crucial information their asymptotic study. In addition, boundedness may fail if not

In this study, a novel stochastic computational frameworks based on fractional Meyer wavelet artificial neural network (FMW-ANN) is designed for nonlinear-singular Lane-Emden (NS-FLE) differential equation. The modeling strength of FMW-ANN used to transformed the NS-FLE system difference equations and approximate theory implemented in mean squared error sense develop merit function equations. M...

In this paper, we consider the problem of the existence of positive weak solutions of { (−∆)su = up in Ω u = 0 on Rn\Ω having prescribed isolated interior singularities. We prove that if n n−2s < p < p1 for some critical exponent p1 defined in the introduction which is related to the stability of the singular solution us, and if S is a closed subset of Ω, then there are infinitely many positive...

Equation (2) has some oscillation behavior [1-3], In 2012, Liu [4] obtained some oscillation criteria of eq. (1). In the last decades, the Emden-Fowler equations have attracted extensive attention for the relevance to nuclear physics and gaseous dynamics in astrophysics, the oscillation behavior of the Emden-Fowler equations are studied by many scholars [5-10]. In this paper, we further study f...