The existence and uniqueness conditions of solution for the problem of multiple parameter nonlocal two points conditions by time variable t for typeless system of differential equations, which contains the value of original solution in the points shifted to the constant value ξi" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgba(0, 0, 0, 0.87); font-family: "Noto Sans", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;"> for the spacial variable x=(x1,...,xp)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgba(0, 0, 0, 0.87); font-family: "Noto Sans", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;"> are established. The solution sought in the scale of Hilbert spaces 2π" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgba(0, 0, 0, 0.87); font-family: "Noto Sans", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;">-periodic for variable x vector functions with exponential behaviour of Fourier coefficients. Solvability of the problem for almost all (except for sets of arbitrarily small measure) values of vector of parameters μ=(μ1,...,μm)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgba(0, 0, 0, 0.87); font-family: "Noto Sans", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;"> in nonlocal conditions are proved. Established lower bounds of small denominators that arise in studying the smoothness of the solution.
- ACS Style
- Ilika, S.A.; Magerovskaya, T.V. Nonlocal problem with many parameters for a system of partial differential equations with shifts. Bukovinian Mathematical Journal. 2018, 2
- AMA Style
- Ilika SA, Magerovskaya TV. Nonlocal problem with many parameters for a system of partial differential equations with shifts. Bukovinian Mathematical Journal. 2018; 2(2-3).
- Chicago/Turabian Style
- Svitlana Anatolyivna Ilika, Tetyana Valeriivna Magerovskaya. 2018. "Nonlocal problem with many parameters for a system of partial differential equations with shifts". Bukovinian Mathematical Journal. 2 no. 2-3.