Goldstein, Gisèle RuizGoldstein, Jerome A.Kömbe, IsmailTellioğlu, Reyhan2023-02-102023-02-102022https://hdl.handle.net/11467/6203https://doi.org/10.1007/s10231-022-01226-6The purpose of this paper is twofold. First is the study of the nonexistence of positive solutions of the parabolic problem {?u?t=?pu+V(x)up-1+?uqin?×(0,T),u(x,0)=u0(x)?0in?,|?u|p-2?u??=?|u|p-2uon??×(0,T),where ? is a bounded domain in RN with smooth boundary ??, ?pu= div (| ? u| p-2? u) is the p-Laplacian of u, V?Lloc1(?), ??Lloc1(??), ?? R, the exponents p and q satisfy 1 < p< 2 , and q> 0. Then, we present some sharp Hardy and Leray type inequalities with remainder terms that provide us concrete potentials to use in the partial differential equation we are interested in.eninfo:eu-repo/semantics/embargoedAccessCritical exponents; Hardy–Leray type inequalities; Nonexistence; Positive solutions; Robin boundary conditionsArticle201629272942Q2WOS:000805733800001N/A2-s2.0-8513133014610.1007/s10231-022-01226-6