{"paper":{"title":"Weak Solutions of a Hyperbolic-Type Partial Dynamic Equation in Banach Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ahmet Yantir, Duygu Soyoglu","submitted_at":"2014-12-23T12:51:48Z","abstract_excerpt":"In this article, we prove an existence theorem regarding the weak solutions to the hyperbolic-type partial dynamic equation \\begin{equation*}\\begin{array}{l}\n  z^{\\Gamma\\Delta}(x,y)=f(x, y, z(x, y)),\n  z(x, 0)=0, \\ \\ \\ z(0, y)=0\n  \\end{array}, \\ \\ x\\in\\mathbb{T}_1, \\ \\ y\\in \\mathbb{T}_2\\end{equation*} in Banach spaces. For this purpose, by generalizing the definitions and results of Cicho\\'n \\emph{et.al.} we develop weak partial derivatives, double integrability and the mean value results for double integrals on time scales. DeBlasi measure of weak noncompactness and Kubiaczyk's fixed point th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7351","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}