On solvability of second-order Sturm-Liouville boundary value problems at resonance

Yujun, Dong

doi:10.1090/S0002-9939-98-04212-9

On solvability of second-order Sturm-Liouville boundary value problems at resonance
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Proc. Amer. Math. Soc. 126 (1998), 145-152 Request permission

Abstract:

In this paper, based on of the concept $q_0\in H_0(p,(0,1),\alpha ,\beta )$, which is a generalized form of the first resonant point $\pi ^2$ to the Picard problem $x''+\lambda x=0$, $x(0)=x(1)=0$, we study the solvability of second-order Sturm-Liouville boundary value problems at resonance $(p(t)x’)’+q_0(t)x+g(t,x)=h(t)$, $x(0){\cos \alpha }-p(0)x’(0)\sin \alpha =0$, $x(1)\cos \beta -p(1)x’(1)\sin \beta =0$, and improve the previous results about problems $x''+\pi ^2x+g(t,x)=h(t),x(0)=x(1)=0$ derived by Chaitan P. Gupta, R. Iannacci and M. N. Nkashama, and Ma Ruyun, respectively.

References

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