On behavior at infinity of solutions of elliptic differential equations in a Banach space

Authors

  • M. L. Gorbachuk Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine; National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 37 Prospect Peremogy, Kyiv, 03056, Ukraine
  • V. M. Gorbachuk National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 37 Prospect Peremogy, Kyiv, 03056, Ukraine 

DOI:

Keywords:

Elliptic differential equation in a Banach space, uniformly and uniformly exponentially stable equation, stable solution, Dirichlet problem, $C_0$-semigroup of linear operators, bounded analytic $C_0$-semigroup, infinitely differentiable, entire, entire of exponential type vectors of a closed operator

Abstract

For a differential equation of the form $y''(t) - By(t) = 0, \ t \in (0, \infty)$, where $B$ is a weakly positive linear operator in a Banach space $\mathfrak{B}$, the conditions on the operator $B$, under which this equation is uniformly or uniformly exponentially stable are given. As distinguished from earlier works dealing only with continuous at 0 solutions, in this paper no conditions on behavior of a solution near 0 are imposed.

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Published

2017-06-25

Issue

Vol. 23 No. 2 (2017)

Section

Articles

How to Cite

Gorbachuk, M. L., and V. M. Gorbachuk. “On Behavior at Infinity of Solutions of Elliptic Differential Equations in a Banach Space”. Methods of Functional Analysis and Topology, vol. 23, no. 2, June 2017, pp. 108-22, https://zen.imath.kiev.ua/index.php/mfat/article/view/657.