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Entire solutions of q-difference equations and value distribution of q-difference polynomials

Jilong Zhang, Lianzhong Yang (2013)

Annales Polonici Mathematici

We investigate the existence and uniqueness of entire solutions of order zero of the nonlinear q-difference equation of the form fⁿ(z) + L(z) = p(z), where p(z) is a polynomial and L(z) is a linear differential-q-difference polynomial of f with small growth coefficients. We also study the zeros distribution of some special type of q-difference polynomials.

Existence results for q-difference inclusions with three-point boundary conditions involving different numbers of q

Sotiris K. Ntouyas, Thanin Sitthiwirattham, Jessada Tariboon (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we study a new class of three-point boundary value problems of nonlinear second-order q-difference inclusions. Our problems contain different numbers of q in derivatives and integrals. By using fixed point theorems, some new existence results are obtained in the cases when the right-hand side has convex as well as noncovex values.

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