The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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SOLVABILITY FOR SECOND-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS ON AN UNBOUNDED DOMAIN AT RESONANCE

  • Yang, Ai-Jun (COLLEGE OF SCIENCE, ZHEJIANG UNIVERSITY OF TECHNOLOGY) ;
  • Wang, Lisheng (SCHOOL OF MATHEMATICS AND PHYSICS, JINGGANGSHAN UNIVERSITY) ;
  • Ge, Weigao (DEPARTMENT OF APPLIED MATHEMATICS, BEIJING INSTITUTE OF TECHNOLOGY)
  • Published : 2010.02.28
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Abstract

This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$ where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.

Keywords

References

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