Dirichlet boundary value problem for differential equations involving dry friction

Boundary value problems

Hana Mach¹  Jan Andres² 

[1] University, Olomouc, Czech Republic;Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký

关键词: Dirichlet problem;    dry friction;    Filippov solution;    Green’s functions;    growth restrictions;    Kakutani-Ky Fan fixed point theorem;    solution estimates;    34A60;    34B15;    34B16;    34B27;    47H04;   

DOI  :  10.1186/s13661-015-0371-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Sufficient conditions in terms of growth restrictions are given for the solvability of the Dirichlet boundary value problem to forced nonlinear differential equations involving the combination of viscous and dry frictions. Explicit estimates of solutions and their derivatives allow us to restrict ourselves to a sufficiently large neighbourhood of the origin, when formulating these effective conditions. In this way, the behaviour of nonlinearities outside of this neighbourhood can be quite arbitrary. In order to get optimal solvability criteria, the problems with one-term and complete linear differential operators will be treated separately by means of various Green’s functions. The obtained results are compared with some of their analogies of the other authors.

【 授权许可】

CC BY