𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Global Existence for Semilinear Evolution Equations with Nonlocal Conditions

✍ Scribed by S.K. Ntouyas; P.Ch. Tsamatos

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
150 KB
Volume
210
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we study the global existence of solutions for semilinear evolution equations with nonlocal conditions, via a fixed point analysis approach. Using the Leray᎐Schauder Alternative, we derive conditions under which a solution exists globally.

πŸ“œ SIMILAR VOLUMES

Global solvability for abstract semiline
Global solvability for abstract semilinear evolution equations
✍ Hirokazu Oka; Naoki Tanaka πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 259 KB

## Abstract The Cauchy problem for the abstract semilinear evolution equation __u__^β€²^(__t__) = __Au__ (__t__) + __B__ (__u__ (__t__)) + __C__ (__u__ (__t__)) is discussed in a general Banach space __X__. Here __A__ is the so‐called Hille‐Yosida operator in __X__, __B__ is a differentiable operator

Existence of Solutions of Nonlinear Diff
Existence of Solutions of Nonlinear Differential Equations with Nonlocal Conditions
✍ M. Benchohra; S.K. Ntouyas πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 69 KB

In this paper we investigate the existence of mild solutions to first order semilinear differential equations in Banach spaces with nonlocal conditions. We shall rely on a fixed point theorem for compact maps due to Schaefer.

Almost global existence for Hamiltonian
Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifolds
✍ D. Bambusi; J.-M. Delort; B. GrΓ©bert; J. Szeftel πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 207 KB πŸ‘ 1 views

## Abstract This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on t