Resonant Problems by Quasilinearization

Table 1

Results of calculations for the boundary value problem 𝑥^′′+𝜋²𝑥=−|𝑥|^𝑝sign𝑥, 𝑥(0)=0=𝑥(1).

𝑝	𝑖	Nonresonant intervals	𝑘	Γ𝑀𝑘	𝑁𝑘
3	1	(0;2√3)	1	1.172	1.814
2	1	(0;2√3)	1	1.196	2.978
3/2	1	(0;2√3)	1	1.748	7.616
4/3	1	(0;2√3)	1	3.071	19.083
	2	(2√3;2√8)	5	219478	298164
	3	(2√8;2√15)	7	2.178⋅10^6	2.245⋅10^6
5/4	1	(0;2√3)	1	5.886	47.492
	2	(2√3;2√8)	5	1.052⋅10^7	1.855⋅10^7
	3	(2√8;2√15)	7	2.045⋅10^8	2.738⋅10^8
	4	(2√15;2√24)	9	1.917⋅10^9	2.044⋅10^9
6/5	1	(0;2√3)	1	11.875	117.828
	2	(2√3;2√8)	5	5.304⋅10^8	11.507⋅10^8
	3	(2√8;2√15)	7	2.021⋅10^10	3.328⋅10^10
	4	(2√15;2√24)	9	3.132⋅10^11	4.108⋅10^11
	5	(2√24;2√35)	11	2.813⋅10^12	3.056⋅10^12
5/6	1	(0;2√3)	1	0.00148	0.00601
	2	(2√3;2√8)	5	1.078⋅10^−11	2.460⋅10^−11
	3	(2√8;2√15)	7	2.506⋅10^−13	4.339⋅10^−13
	4	(2√15;2√24)	9	1.541⋅10^−14	2.127⋅10^−14
	5	(2√24;2√35)	11	1.675⋅10^−15	1.914⋅10^−15
4/5	1	(0;2√3)	1	0.0017	0.0149
	2	(2√3;2√8)	5	8.132⋅10^−10	15.264⋅10^−10
	3	(2√8;2√15)	7	3.706⋅10^−11	5.277⋅10^−11
	4	(2√15;2√24)	9	3.767⋅10^−12	4.275⋅10^−12
3/4	1	(0;2√3)	1	0.0055	0.0371
	2	(2√3;2√8)	5	6.459⋅10^−8	9.502⋅10^−8
	3	(2√8;2√15)	7	5.768⋅10^−9	6.439⋅10^−9
2/3	1	(0;2√3)	1	0.0191	0.0931
1/6	1	(0;2√3)	1	0.382	0.566