We prove some results about the existence of fixed points, periodic points and chaotic-like dynamics for a class of planar maps which satisfy a suitable property of “arc expansion” type. We also outline some applications to the nonlinear Hill’s equations with indefinite weight. 2000 Mathematics Subject Classification: 34C15, 34C25, 34C28, 37D45, 70KXX, 70K40.

We consider a diffusive p–logistic equation in the whole of R with absorption and an indefinite weight. Using variational and truncation techniques we prove a bifurcation theorem and describe completely the bifurcation point. In the semilinear case p = 2, under an additional hypothesis on the absorption term, we show that the positive solution is unique.

Gosper’s summation algorithm finds a hypergeometric closed form of an indefinite sum of hypergeometric terms, if such a closed form exists. We extend his algorithm to the case when the terms are simultaneously hypergeometric and multibasic hypergeometric. We also provide algorithms for finding polynomial as well as hypergeometric solutions of recurrences in the mixed case. We do not require the...

In this article, we establish the existence and non-existence of solutions for quasilinear equations with nonlinear boundary conditions and indefinite weight. Our proofs are based on variational methods and their geometrical features. In addition, we prove that all the weak solutions are in C1,β(Ω) for some β ∈ (0, 1).

by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...