{"title":"Some Remarks on Multiplier Spaces I: Classical Spaces","authors":"D. Bugajewska, S. Reinwand","doi":"10.4171/ZAA/1631","DOIUrl":"https://doi.org/10.4171/ZAA/1631","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1631","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42070181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms $$ dot{x}(t)+ sum_{k=1}^m a_k(t)x(h_k(t))- sum_{k=1}^l b_k(t)x(g_k(t))=0 $$ and its modifications, and apply them to investigate local stability of Mackey--Glass type models $$dot{x}(t)=r(t)left[betafrac{x(g(t))}{1+x^n(g(t))}-gamma x(h(t))right]$$ and $$dot{x}(t)=r(t)left[betafrac{x(g(t))}{1+x^n(h(t))}-gamma x(t)right].$$
{"title":"On Stability of Delay Equations with Positive and Negative Coefficients with Applications","authors":"L. Berezansky, Eric P. Braverman","doi":"10.4171/ZAA/1633","DOIUrl":"https://doi.org/10.4171/ZAA/1633","url":null,"abstract":"We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms $$ dot{x}(t)+ sum_{k=1}^m a_k(t)x(h_k(t))- sum_{k=1}^l b_k(t)x(g_k(t))=0 $$ and its modifications, and apply them to investigate local stability of Mackey--Glass type models $$dot{x}(t)=r(t)left[betafrac{x(g(t))}{1+x^n(g(t))}-gamma x(h(t))right]$$ and $$dot{x}(t)=r(t)left[betafrac{x(g(t))}{1+x^n(h(t))}-gamma x(t)right].$$","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1633","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41512201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Nonlinear Klein–Gordon– Maxwell System in $mathbb{R}^{2}$ Involving Singular and Vanishing Potentials","authors":"Lin Li, F. Albuquerque","doi":"10.4171/ZAA/1636","DOIUrl":"https://doi.org/10.4171/ZAA/1636","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1636","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47770515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Existence Results for the Klein–Gordon–Maxwell System in Rotationally Symmetric Bounded Domains","authors":"Yuhu Wu, B. Ge, O. Miyagaki","doi":"10.4171/ZAA/1635","DOIUrl":"https://doi.org/10.4171/ZAA/1635","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1635","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42663849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Semilinear Mixed Type Integro-Differential Evolution Equations via Kuratowski Measure of Noncompactness","authors":"M. Benchohra, N. Rezoug, Yong Zhou","doi":"10.4171/ZAA/1623","DOIUrl":"https://doi.org/10.4171/ZAA/1623","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1623","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41998495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Araujo, Luiz F. O. Faria, E. Leite, O. Miyagaki
In this paper, we study strongly coupled elliptic systems in non-variational form with negative exponents involving fractional Laplace operators. We investigate the existence, nonexistence, and uniqueness of the positive classical solution. The results obtained here are a natural extension of the results obtained by Ghergu (2010), for the fractional case.
{"title":"Positive Solutions for Non-Variational Fractional Elliptic Systems with Negative Exponents","authors":"A. Araujo, Luiz F. O. Faria, E. Leite, O. Miyagaki","doi":"10.4171/ZAA/1675","DOIUrl":"https://doi.org/10.4171/ZAA/1675","url":null,"abstract":"In this paper, we study strongly coupled elliptic systems in non-variational form with negative exponents involving fractional Laplace operators. We investigate the existence, nonexistence, and uniqueness of the positive classical solution. The results obtained here are a natural extension of the results obtained by Ghergu (2010), for the fractional case.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43043686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stimulated by the category theorems of Eisner and Ser'eny in the setting of unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove category theorems for Schr"odinger semigroups. Specifically, we show that, to a given class of Schr"{o}dinger semigroups, Baire generically the semigroups are strongly stable but not exponentially stable. We also present a typical spectral property of the corresponding Schr"{o}dinger operators.
{"title":"Category Theorems for Schrödinger Semigroups","authors":"M. Aloisio, S. L. Carvalho, C. Oliveira","doi":"10.4171/zaa/1666","DOIUrl":"https://doi.org/10.4171/zaa/1666","url":null,"abstract":"Stimulated by the category theorems of Eisner and Ser'eny in the setting of unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove category theorems for Schr\"odinger semigroups. Specifically, we show that, to a given class of Schr\"{o}dinger semigroups, Baire generically the semigroups are strongly stable but not exponentially stable. We also present a typical spectral property of the corresponding Schr\"{o}dinger operators.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43722521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global Bifurcation of Positive Solutions of Semi-Linear Elliptic Partial Differential Equations with Indefinite Weight","authors":"Z. Aliyev, S. M. Hasanova","doi":"10.4171/ZAA/1625","DOIUrl":"https://doi.org/10.4171/ZAA/1625","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1625","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49579033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the Dirichlet φ-energy integral with Sobolev boundary values. The function φ has generalized Orlicz growth. Special cases include variable exponent and double phase growths. We show that minimizers are regular at the boundary provided a weak capacity fatness condition is satisfied. This condition is satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.
{"title":"Boundary Regularity under Generalized Growth Conditions","authors":"Petteri Harjulehto, P. Hästö","doi":"10.4171/ZAA/1628","DOIUrl":"https://doi.org/10.4171/ZAA/1628","url":null,"abstract":"We study the Dirichlet φ-energy integral with Sobolev boundary values. The function φ has generalized Orlicz growth. Special cases include variable exponent and double phase growths. We show that minimizers are regular at the boundary provided a weak capacity fatness condition is satisfied. This condition is satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1628","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49668367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Lyapunov Type Inequality for a Nonlinear Fractional Hybrid Boundary Value Problem","authors":"B. López, Juan Rocha, K. Sadarangani","doi":"10.4171/ZAA/1629","DOIUrl":"https://doi.org/10.4171/ZAA/1629","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"3 5","pages":""},"PeriodicalIF":1.2,"publicationDate":"2019-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1629","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41260775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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