Qualitative behaviour of solutions of the Goursat problem for hyperbolic differential equations
This work is an extension of the studies on solutions of the Goursat problem in the quarter space to the case in the domain: \(D=\{(x,y):\quad x\geq 0,0\leq y\leq g(x)\},\) where g is strictly increasing. Specifically the problem treated here is to establish oscillation criteria and to determine the asymptotic behavior of solutions of the problem \[ u_{xy}+p(x,y)u=0,\quad x>0,\quad 0<y<g(x),\quad u(x,0)=\phi (x),\quad x>0,\quad u(x,g(x))=\psi (x),\quad x>0. \] The author shows the existence of non-oscillatory solution as well as an oscillatory criteria.
scientific article; zbMATH DE number 4065528
scientific article