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By employing Mawhin’s continuation theorem, the existence of periodic solutions of the p-Laplacian Liénard equation with a deviating argument (φp(x′(t)))′ + f(x(t))x′(t) + g(x(t− τ(t))) = e(t) under various assumptions are obtained. Keywords—periodic solution, Mawhin’s continuation theorem, deviating argument.
As indicated by Pachpatte , this result has been frequently used by authors to obtain global existence, uniqueness and stability of solutions of various nonlinear integral and differential equations. On the other hand, Theorem 1.1 has also been extended and generalized by many authors; see, for example, the reference [2, 3, 6, 7, 8, 9, 13, 14, 15, 17,… (More)
Some discrete analogue of Poincaré-type integral inequalities involving many functions of many independent variables are established. These in turn can serve as generators of further interesting discrete inequalities. 2000 Mathematics Subject Classification. Primary 39A10, 39A12, 39B72.
Some generalized Hölder’s inequalities for positive as well as negative exponents are obtained. 2000 Mathematics Subject Classification. 26D07, 26D15.
By employing Mawhin’s continuation theorem, the existence of periodic solutions of the p-Laplacian generalized Liénard equation with deviating argument (φp(x′(t)))′ + f(t, x(t))x′(t) + β(t)g(x(t− τ(t))) = e(t) under various assumptions are obtained. Keywords—periodic solution, Mawhin’s continuation theorem, deviating argument.
This is a survey and expository article. Some new developments on refinements, generalizations, applications of Jordan’s inequality and related problems, including some results about Wilker-Anglesio’s inequality, some estimates for three kinds of complete elliptic integrals and several inequalities for the remainder of power series expansion of ex, are… (More)