Existence and NonExistence for the Collision-Induced Breakage Equation

Existence and Nonexistence of Solutionsfor

Harmonic Homeomorphisms: Existence and Nonexistence

These notes were prepared for International Workshop on Harmonic and Quasiconformal Mappings in Chennai, August 2010. They are based on several papers written jointly with Tadeusz Iwaniec, Jani Onninen, and Ngin-Tee Koh. The source papers are available from www.arxiv.org

Existence and nonexistence of positive solution for sixth-order boundary value problems

‎In this paper‎, ‎we formulate the sixth-order boundary value problem as Fredholm integral equation by finding Green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problem‎. ‎Also nonexistence results are obtained‎. ‎An example is given to illustrate the results of paper‎.

Existence and Nonexistence of Entire Solutions to the Logistic Differential Equation

We consider the one-dimensional logistic problem (rαA(|u′|)u′)′ = rαp(r) f (u) on (0,∞), u(0) > 0, u′(0)= 0, where α is a positive constant and A is a continuous function such that the mapping tA(|t|) is increasing on (0,∞). The framework includes the case where f and p are continuous and positive on (0,∞), f (0) = 0, and f is nondecreasing. Our first purpose is to establish a general nonexiste...

Existence and Nonexistence of Descriptive Patterns

In the present paper, we study the existence of descriptive patterns, i. e. patterns that cover all words in a given set through morphisms and that are optimal in terms of revealing commonalities of these words. Our main result shows that if patterns may be mapped onto words by arbitrary morphisms, then there exist infinite sets of words that do not have a descriptive pattern. This answers a qu...