The Lane-Emden equation has been used to model several phenomenas in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the Rational Chebyshev of Second Kind function (RSC) to solve the Lane-Emden equation over the semi-infinit interval [0,+∞). According to well-known results and com...

By using the Riccati technique, which reduces higher order dynamic equations to a inequality, we will establish some new sufficient conditions for oscillation of half-linear/Emden-Fowler neutral equation form \[ (r(\varrho)((\mathbf{\mathbf{x}}(\varrho)+p(\varrho)\mathbf{x}(\tau (\varrho)))^{\Delta })^{\gamma })^{\Delta }+q(\varrho)\mathbf{x}^{a }(\delta (\varrho))+v(\varrho)\mathbf{x}^{\beta }...

In this article, we present a collocation method for second-order nonlinear Lane-Emden type pantograph differential equations under intial conditions. According to the method, solution of problem is sought depending on Pell-Lucas polynomials. The polynomials are written in matrix form based standard bases. Then, and its derivatives also forms. Next, transformation constituted proportion delay f...