Sharp conditions for the existence of positive solutions for a second-order singular impulsive differential equation

Abstract

Using a transformation technique to deal with the impulse term of a second-order singular impulsive differential equation, this paper establishes sharp conditions to guarantee the existence of $C^1[0,1]$ positive solutions. The results significantly extend and improve many known results for both the continuous case and more general nonsingular case.

Keywords:

• Singularity
• $C^1[0</Keyword><Keyword>1]$ positive solutions of impulsive differential equations
• transformation technique
• $L^p$-integrable; Sharp conditions

AMS Subject Classifications:

• 34B18
• 34C23
• 34K10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is sponsored by the National Natural Science Foundation of China [grant number 11301178], [grant number 11371117], the Beijing Natural Science Foundation of China [grant number 1163007] and the Scientific Research Project of Construction for Scientific and Technological Innovation Service [grant number 71E1610973].