We prove L1{contraction principle and uniqueness of solutions for quasilinear elliptic{parabolic equations of the form @t[b(u)] div[a(ru; b(u))] + f(b(u)) = 0 in (0; T ) ; where b is monotone nondecreasing and continuous. We only assume that u is a weak solution of nite energy (see [1]). In particular, we do not suppose that the distributional derivative @t[b(u)] is a bounded Borel measure or a...

Article history: Received 19 February 2009 Received in revised form 28 October 2011 Accepted 21 December 2011 Available online 23 December 2011

In this paper we deal with a first order evolution inclusion involving multivalued term generated by Clarke subdifferential of locally Lipschitz potential. For problem construct double step time-semidiscrete approximation, known as the Rothe scheme. We study sequence solutions semidiscrete approximate problems and provide its weak convergence to limit element that is solution original problem.

If all the forces o f nature can be reduced to those which follow from a linear combination o f a scalar and vector potential, as in electrodynamics, Lorentz invariance can be derived as a dynamic symmetry. All that has to be done is to assume that there is an all pervading substratum or ether, transmitting those forces through space, and that all physical bodies actually observed are held toge...

Plasmodial fragments of Physarum polycephalum, excised from anterior regions of a thin-spread plasmodium, contracted-relaxed cyclicly with a period of 3-5 min. The area of the fragments decreased approximately 10% during contraction. In most cases, there was little endoplasmic streaming which indicates that contractions were synchronized throughout the fragment. By both polarized light and fluo...

* Correspondence: ming@mail. nhcue.edu.tw Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan Full list of author information is available at the end of the article Abstract In this article, we introduce the notions of (j φ)-weak contraction mappings and (ψ φ)-weak contraction mappings in complete generalized metric spaces and prove two theorems which a...

by generalizing the well known guiding function method. Such an approach can be found in several works, however, under some heavier assumptions. For example, in [M] f is assumed to be locally lipschitzian and the guiding function to be C. In [GP] f needs to be of the Caratheodory type only, while the corresponding guiding function must be still C. In fact, in [GP] the more general, multivalued ...