The aim of this paper is to present new summation inequalities and to show that the half-linear difference equation Delta (a(n) \Deltaxn\ alpha sgn Deltaxn,) = bn \x(n+1)\alpha sgn x(n+1) exhibits not only similarities but also some discrepancies with the linear case, especially as regards the possible coexistence of the so-called extremal solutions. Some of our results are new also for the linear difference equation.
Summation inequalities and half-linear difference equations / M. CECCHI;Z. DOSLA; M. MARINI;I. VRKOC. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 302:(2005), pp. 1-13. [10.1016/j.jmaa.2004.08.005]
Summation inequalities and half-linear difference equations
MARINI, MAURO;
2005
Abstract
The aim of this paper is to present new summation inequalities and to show that the half-linear difference equation Delta (a(n) \Deltaxn\ alpha sgn Deltaxn,) = bn \x(n+1)\alpha sgn x(n+1) exhibits not only similarities but also some discrepancies with the linear case, especially as regards the possible coexistence of the so-called extremal solutions. Some of our results are new also for the linear difference equation.
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