Pith Number

pith:2ZXRTNDD

pith:2025:2ZXRTNDDIFSW656QNMUOI7IDCL

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On the existence of solutions of dynamic equations on time scales in Banach spaces

Du\v{s}an Oberta

Dynamic equations on arbitrary time scales in Banach spaces have solutions when a new Kamke Δ-function and measures of noncompactness control compactness.

arxiv:2512.13602 v2 · 2025-12-15 · math.FA · math.CA

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\pithnumber{2ZXRTNDDIFSW656QNMUOI7IDCL}

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel (1980), to an arbitrary time scale.

C2weakest assumption

The newly introduced Kamke Δ-function satisfies the required properties on an arbitrary time scale; this is asserted but its verification for general time scales is not shown in the abstract.

C3one line summary

Existence theorems are established for dynamic equations on time scales in Banach spaces via measures of noncompactness and a new Kamke Δ-function.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] Ahmed A.A.H., Hazarika B.: On solvability of dynamic equation in Banach space of continuous functions over time scales. Filomat 38, no. 12, 4035–4044 (2024) 2024

[2] Ambrosetti A.: Un teorema di esistenza per le equazioni differenziali negli spazi di Banach. Rend. Sem. Mat. Univ. Padova 39, 349–361 (1967) 1967

[3] Lecture Notes in Pure and Applied Mathematics, 60 1980

[4] Bana ´s J., Lecko M.: Solvability of infinite systems of differential equations in Banach sequence spaces. J. Comput. Appl. Math. 137(2), 363–375 (2001) 2001

[5] Springer, New Delhi (2014) 2014

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-09T01:05:11.769158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d66f19b46341656f77d06b28e47d0312c17dadb0b8063cc05596ef8d51c0d915

Aliases

arxiv: 2512.13602 · arxiv_version: 2512.13602v2 · doi: 10.48550/arxiv.2512.13602 · pith_short_12: 2ZXRTNDDIFSW · pith_short_16: 2ZXRTNDDIFSW656Q · pith_short_8: 2ZXRTNDD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2ZXRTNDDIFSW656QNMUOI7IDCL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d66f19b46341656f77d06b28e47d0312c17dadb0b8063cc05596ef8d51c0d915

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a254f08ad0829ced4c13deed926cea20166c6f027edc927aeb5fd8df8bf0739e",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-12-15T17:55:33Z",
    "title_canon_sha256": "a0ae27551cbaea8fd8a68280352b664ffb5ee78cf7420d85df752e6a3dfc2e44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.13602",
    "kind": "arxiv",
    "version": 2
  }
}