一类p-Laplacian方程多点边值问题共振情况下解的存在性

he p-laplacian equation is widely used in fields such as non-linear elasticity, glaciology, combustion theory, biology and a variety of non-linear fluid, and has important theoretical and practical value. Most studies of the p-Laplacian equation is multi-point boundary value problem in the non-resonance case, there exist few essays discussing the existence of solutions at resonance. In order to study the existence of solutions for multi-point boundary value problems with p-Laplacian at resonance, by means of theory of coincidence degree, sufficient conditions for the existence of at least one solution are established, and spread the conclusion from m points to double m points.