Existence of bounded solutions of integral boundary value problems for singular differential equations on whole lines
The authors prove the existence of solution to the following boundary value problem on the whole line: NEWLINE\[NEWLINE[\Phi(\rho(t)\,x'(t))]'+f(t,x(t),x'(t))=0, \quad t \in \mathbb R,NEWLINE\]NEWLINE NEWLINE\[NEWLINE\lim_{t \to - \infty}{x(t)}=\int_{-\infty}^{+ \infty}{g(s,x(s),x'(s))\, ds},NEWLINE\]NEWLINE NEWLINE\[NEWLINE\lim_{t \to + \infty}{x(t)}=\int_{-\infty}^{+ \infty}{h(s,x(s),x'(s))\, ds},NEWLINE\]NEWLINE where the involved functions satisfy suitable properties.NEWLINENEWLINEThe results follow from fixed point theory and some approximation procedure.
scientific article; zbMATH DE number 6359571