The present paper is concerned with the existence of solutions for a $\phi-$Laplacian nonlinear boundary value problem (bvp) set on the half-line of second-order differential equation: \begin{equation*} (\phi (r'(t)))' +g(t,r(t),r'(t))=0 ,\quad\text{a.e. } t\in [ 0,+\infty )\backslash \{t_{1},t_{2},\ldots\}, \end{equation*} with the boundary conditions, \begin{equation*} r(0)=A,\quad r'(+\infty )=B, \end{equation*} where $g:[0,+\infty )\times \mathbb{R}^{2}\to \mathbb{R}$ is an $L^{1}$-Carath\'eodory function, and the impulsive conditions are Carathéodory sequences. We use the Schauder fixed point theorem to get our result. The application of the result in an illustrative example of the disappearance of one body and the appearance of another at intervals of time, such as what happens in particle physics (for example the nuclear fission and fusion) and quantum mechanics (Compton scattering).
2020 Mathematics Subject Classification: 34B37, 34B15, 34A36.