Задача Штурма-Лиувилля. Молчанова Л.А. - 7 стр.

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y
00
+ λy = 0, y(0) = 0, y(l) = 0, x ∈ [0, l];
y
00
+ λy = 0, y(0) = 0, y
0
(l) + hy(l) = 0, x ∈ [0, l], h > 0;
y
00
+ λy = 0, y(l) = 0, −y
0
(0) + hy(0) = 0, x ∈ [0, l], h > 0;
y
00
+ λy = 0, y(0) = 0, y
0
(l) = 0, x ∈ [0, l];
y
00
+ λy = 0, y
0
(0) = 0, y(l) = 0, x ∈ [0, l];
y
00
+ λy = 0, y
0
(0) = 0, y
0
(l) = 0, x ∈ [0, l];
y
00
+ λy = 0, y
0
(0) = 0, y
0
(l) + hy(l) = 0, x ∈ [0, l], h > 0;
y
00
+ λy = 0, y
0
(l) = 0, −y
0
(0) + hy(0) = 0, x ∈ [0, l], h > 0;
y
00
+ λy = 0, −y
0
(0) + hy(0) = 0, y
0
(l) + hy(l) = 0, x ∈ [0, l], h > 0;
(xy
0
)
0
+ λ/xy = 0, y(a) = 0, y(b) = 0, x ∈ [a, b], a 6= 0, b 6= 0;
(x
2
y
0
)
0
+ λx
2
y = 0, y(a) = 0, y(b) = 0, x ∈ [ a, b], a 6= 0, b 6= 0;
y
00
+ λy = 0, y(−l) = 0, y(l) = 0, x ∈ [−l, l];
y
00
+ λy = 0, y
0
(−l) = 0, y
0
(l) = 0, x ∈ [−l, l];
y
00
+ λy = 0, −y
0
(−l) + hy(−l)=0, y
0
(l) + hy(l)=0, x ∈ [−l, l], h > 0;
(xy
0
)
0
+ λ/xy = 0, y
0
(a) = 0, y
0
(b) = 0, x ∈ [a, b], a 6= 0, b 6= 0;
((x + 0.2 cos πx)y
0
)
0
+ λy = 0, y(0) − y
0
(0) = 0, y(1) = 0, x ∈ [0, 1];
((x + 0.2 cos πx)y
0
)
0
+ λy = 0, y(0) = 0, y(1) + y
0
(1) = 0, x ∈ [0, 1];
((x + 0.2 cos πx)y
0
)
0
+ λy = 0, y(0) − y
0
(0) = 0 y
0
(1) = 0, x ∈ [0, 1];
((x + 0.2 cos πx)y
0
)
0
+ λy = 0, y
0
(0) = 0 y(1) + y
0
(1) = 0, x ∈ [0, 1];
((x + 0.2 cos πx)y
0
)
0
+ λy = 0, y(0) = 0 y(1) + y
0
(1) = 0, x ∈ [0, 1];
((x + 0.2 cos πx)y
0
)
0
+ λy = 0, 2y(0) + y
0
(0) = 0 y(1) = 0, x ∈ [0, 1];
((x + 0.2 cos πx)y
0
)
0
+ λy = 0, y(0) − y
0
(0) = 0, y(1) = 0, x ∈ [0, 1];
((4x + cos πx)y
0
)
0
+ λy = 0, y(0) = 0, y(1) + y
0
(1) = 0, x ∈ [0, 1];
((4x + cos πx)y
0
)
0
+ λy = 0, y(0) − y
0
(0) = 0 y
0
(1) = 0, x ∈ [0, 1];
((4x + cos πx)y
0
)
0
+ λy = 0, y
0
(0) = 0 y(1) + y
0
(1) = 0, x ∈ [0, 1].
Çàäàíèÿ
1 Íàéòè ñîáñòâåííûå çíà÷åíèÿ è ñîáñòâåííûå ôóíêöèè êðàåâîé çàäà÷è

      1. y 00 + λy = 0, y(0) = 0, y(l) = 0, x ∈ [0, l];
      2. y 00 + λy = 0, y(0) = 0, y 0 (l) + hy(l) = 0, x ∈ [0, l], h > 0;
      3. y 00 + λy = 0, y(l) = 0, −y 0 (0) + hy(0) = 0, x ∈ [0, l], h > 0;
      4. y 00 + λy = 0, y(0) = 0, y 0 (l) = 0, x ∈ [0, l];
      5. y 00 + λy = 0, y 0 (0) = 0, y(l) = 0, x ∈ [0, l];
      6. y 00 + λy = 0, y 0 (0) = 0, y 0 (l) = 0, x ∈ [0, l];
      7. y 00 + λy = 0, y 0 (0) = 0, y 0 (l) + hy(l) = 0, x ∈ [0, l], h > 0;
      8. y 00 + λy = 0, y 0 (l) = 0, −y 0 (0) + hy(0) = 0, x ∈ [0, l], h > 0;
      9. y 00 + λy = 0, −y 0 (0) + hy(0) = 0, y 0 (l) + hy(l) = 0, x ∈ [0, l], h > 0;
     10. (xy 0 )0 + λ/xy = 0, y(a) = 0, y(b) = 0, x ∈ [a, b], a 6= 0, b 6= 0;
     11. (x2 y 0 )0 + λx2 y = 0, y(a) = 0, y(b) = 0, x ∈ [a, b], a 6= 0, b 6= 0;
     12. y 00 + λy = 0, y(−l) = 0, y(l) = 0, x ∈ [−l, l];
     13. y 00 + λy = 0, y 0 (−l) = 0, y 0 (l) = 0, x ∈ [−l, l];
     14. y 00 + λy = 0, −y 0 (−l) + hy(−l)=0, y 0 (l) + hy(l)=0, x ∈ [−l, l], h > 0;
     15. (xy 0 )0 + λ/xy = 0, y 0 (a) = 0, y 0 (b) = 0, x ∈ [a, b], a 6= 0, b 6= 0;
     16. ((x + 0.2 cos πx)y 0 )0 + λy = 0, y(0) − y 0 (0) = 0, y(1) = 0, x ∈ [0, 1];
     17. ((x + 0.2 cos πx)y 0 )0 + λy = 0, y(0) = 0, y(1) + y 0 (1) = 0, x ∈ [0, 1];
     18. ((x + 0.2 cos πx)y 0 )0 + λy = 0, y(0) − y 0 (0) = 0 y 0 (1) = 0, x ∈ [0, 1];
     19. ((x + 0.2 cos πx)y 0 )0 + λy = 0, y 0 (0) = 0 y(1) + y 0 (1) = 0, x ∈ [0, 1];
     20. ((x + 0.2 cos πx)y 0 )0 + λy = 0, y(0) = 0 y(1) + y 0 (1) = 0, x ∈ [0, 1];
     21. ((x + 0.2 cos πx)y 0 )0 + λy = 0, 2y(0) + y 0 (0) = 0 y(1) = 0, x ∈ [0, 1];
     22. ((x + 0.2 cos πx)y 0 )0 + λy = 0, y(0) − y 0 (0) = 0, y(1) = 0, x ∈ [0, 1];
     23. ((4x + cos πx)y 0 )0 + λy = 0, y(0) = 0, y(1) + y 0 (1) = 0, x ∈ [0, 1];
     24. ((4x + cos πx)y 0 )0 + λy = 0, y(0) − y 0 (0) = 0 y 0 (1) = 0, x ∈ [0, 1];
     25. ((4x + cos πx)y 0 )0 + λy = 0, y 0 (0) = 0 y(1) + y 0 (1) = 0, x ∈ [0, 1].


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