半直线上一类带有积分边值条件的多点边值问题在共振情形下的可解性OA
Solvability of a class of multi-point boundary value problem with integral boundary conditions on a half-line at resonance
运用Mawhin重合度理论,讨论了半直线上一类带有积分边值条件的三阶多点边值问题{(q(t)u"(t))'=g(t,u(t),u'(t),u"(t)),t∈[0,∞),{u(0)=m∑i=1αi∫ξi0u(t)dt,{u'(0)=n∑j=1βj∫ηj0u'(t)dt,{limt→+∞q(t)u"(t)=0在共振情形下的可解性,其中g:[0,1]×R3→R满足L1[0,∞)-Carathéodory条件,αi、βj、ξi、ηj∈R(1≤i≤m,1≤j≤n,m、n∈Z+),q(t)＞0,q(t)∈ C[0,∞)∩C2(0,∞),1/q(t)∈ L1[0,∞),获得了该边值问题至少存在 1 个解的充分条件.
By using Mawhin coincidence degree theorey,the solvability of a class of third-order multi-point boundary value problems{(q(t)u"(t))'=g(t,u(t),u'(t),u"(t)),t ∈[0,∞),{u(0)=m∑i=1αi∫ξi0u(t)dt,{u'(0)=n∑j=1βj∫ηj0u'(t)dt,{limt→+∞ q(t)u"(t)=0 at resonance on half-line is discussed,where g:[0,1]×R3→R satisfies L1[0,∞)-Carathéodory conditions,αi,βj,ξi,ηj∈R(1≤i≤m,1≤j≤n,m,n∈Z+),q(t)＞0,q(t)∈ C[0,∞)R∩C2(0,∞),1/q(t)∈L1[0,∞),and obtained sufficient conditions for the existence of at least one solution to this boundary value problem.
杜睿娟
甘肃政法大学人工智能学院,甘肃兰州
数理科学
积分边值条件共振Mawhin重合度半直线
integral boundary conditionsresonanceMawhin coincidence degreehalf-line
《北京师范大学学报（自然科学版）》 2026 (1)
8-15,8
国家自然科学基金资助项目(12461039)2025年甘肃省大学生就业创业能力提升资助项目(523/000029918)2023年甘肃省高等教育教学成果培育资助项目(161/001011001)甘肃政法大学第二批课堂教学改革资助项目(399/202400107)
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