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Leray–Schauder degree

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or equivalently to boundary-sphere-preserving continuous maps between balls
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is some compact map (i.e. mapping bounded sets to sets whose closure is
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to prove existence results for partial differential equations.
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to boundary-sphere-preserving maps between balls in a
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Annales scientifiques de l'École normale supérieure
468:Mawhin, J. (2018). A tribute to Juliusz Schauder. 358: 334: 311: 276: 182:{\displaystyle (B^{n},S^{n-1})\to (B^{n},S^{n-1})} 181: 91: 529: 8: 277:{\displaystyle f:(B(V),S(V))\to (B(V),S(V))} 536: 522: 445:Topological Methods in Nonlinear Analysis 415: 351: 324: 289: 197: 164: 151: 126: 113: 104: 74: 49: 40: 400:"Topologie et équations fonctionnelles" 390: 284:, assuming that the map is of the form 92:{\displaystyle (S^{n},*)\to (S^{n},*)} 398:Leray, Jean; Schauder, Jules (1934). 7: 490: 488: 24:is an extension of the degree of a 14: 492: 271: 268: 262: 253: 247: 241: 238: 235: 232: 226: 217: 211: 205: 176: 144: 141: 138: 106: 86: 67: 64: 61: 42: 1: 508:. You can help Knowledge by 373:The degree was invented by 576: 487: 471:Antiquitates Mathematicae 360: 336: 313: 312:{\displaystyle f=id-C} 278: 183: 93: 439:Mawhin, Jean (1999). 361: 337: 314: 279: 184: 94: 22:Leray–Schauder degree 350: 323: 288: 196: 103: 39: 417:10.24033/asens.836 356: 335:{\displaystyle id} 332: 309: 274: 179: 89: 517: 516: 359:{\displaystyle C} 567: 538: 531: 524: 502:topology-related 496: 489: 479: 466: 460: 459: 457: 456: 436: 430: 429: 419: 395: 379:Juliusz Schauder 365: 363: 362: 357: 341: 339: 338: 333: 318: 316: 315: 310: 283: 281: 280: 275: 188: 186: 185: 180: 175: 174: 156: 155: 137: 136: 118: 117: 98: 96: 95: 90: 79: 78: 54: 53: 575: 574: 570: 569: 568: 566: 565: 564: 545: 544: 543: 542: 485: 483: 482: 467: 463: 454: 452: 438: 437: 433: 397: 396: 392: 387: 348: 347: 321: 320: 286: 285: 194: 193: 160: 147: 122: 109: 101: 100: 70: 45: 37: 36: 12: 11: 5: 573: 571: 563: 562: 560:Topology stubs 557: 547: 546: 541: 540: 533: 526: 518: 515: 514: 497: 481: 480: 461: 431: 389: 388: 386: 383: 355: 331: 328: 308: 305: 302: 299: 296: 293: 273: 270: 267: 264: 261: 258: 255: 252: 249: 246: 243: 240: 237: 234: 231: 228: 225: 222: 219: 216: 213: 210: 207: 204: 201: 178: 173: 170: 167: 163: 159: 154: 150: 146: 143: 140: 135: 132: 129: 125: 121: 116: 112: 108: 88: 85: 82: 77: 73: 69: 66: 63: 60: 57: 52: 48: 44: 30:continuous map 13: 10: 9: 6: 4: 3: 2: 572: 561: 558: 556: 553: 552: 550: 539: 534: 532: 527: 525: 520: 519: 513: 511: 507: 504:article is a 503: 498: 495: 491: 486: 477: 473: 472: 465: 462: 450: 446: 442: 435: 432: 427: 423: 418: 413: 409: 405: 401: 394: 391: 384: 382: 380: 376: 371: 369: 353: 345: 329: 326: 306: 303: 300: 297: 294: 291: 265: 259: 256: 250: 244: 229: 223: 220: 214: 208: 202: 199: 192: 171: 168: 165: 161: 157: 152: 148: 133: 130: 127: 123: 119: 114: 110: 83: 80: 75: 71: 58: 55: 50: 46: 35: 31: 27: 23: 19: 510:expanding it 499: 484: 475: 469: 464: 453:. Retrieved 448: 444: 434: 407: 403: 393: 372: 344:identity map 191:Banach space 21: 15: 28:preserving 18:mathematics 549:Categories 455:2022-04-19 385:References 375:Jean Leray 26:base point 451:: 195–228 426:0012-9593 410:: 45–78. 304:− 239:→ 169:− 142:→ 131:− 84:∗ 65:→ 59:∗ 555:Topology 32:between 368:compact 342:is the 34:spheres 424:  319:where 20:, the 500:This 506:stub 422:ISSN 377:and 346:and 412:doi 370:). 16:In 551:: 476:12 474:, 449:14 447:. 443:. 420:. 408:51 406:. 402:. 537:e 530:t 523:v 512:. 478:. 458:. 428:. 414:: 354:C 330:d 327:i 307:C 301:d 298:i 295:= 292:f 272:) 269:) 266:V 263:( 260:S 257:, 254:) 251:V 248:( 245:B 242:( 236:) 233:) 230:V 227:( 224:S 221:, 218:) 215:V 212:( 209:B 206:( 203:: 200:f 177:) 172:1 166:n 162:S 158:, 153:n 149:B 145:( 139:) 134:1 128:n 124:S 120:, 115:n 111:B 107:( 87:) 81:, 76:n 72:S 68:( 62:) 56:, 51:n 47:S 43:(

Index

mathematics
base point
continuous map
spheres
Banach space
identity map
compact
Jean Leray
Juliusz Schauder
"Topologie et équations fonctionnelles"
doi
10.24033/asens.836
ISSN
0012-9593
"Leray-Schauder degree: a half century of extensions and applications"
Antiquitates Mathematicae
Stub icon
topology-related
stub
expanding it
v
t
e
Categories
Topology
Topology stubs

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