Wirtinger inequality and nonlinear differential systems
نویسندگان
چکیده
منابع مشابه
Wirtinger Inequality and Nonlinear Differential Systems
Picone identity for a class of nonlinear differential equations is established and various qualitative results (such as Wirtinger-type inequality and the existence of zeros of first components of solutions) are obtained with the help of this new formula.
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Let α (p, q, r) = inf (ku0kp kukq : u ∈W 1,p per (−1, 1) \ {0} , Z 1 −1 |u|r−2 u = 0 ) . We show that α (p, q, r) = α (p, q, q) if q ≤ rp+ r − 1 α (p, q, r) < α (p, q, q) if q > (2r − 1) p generalizing results of Dacorogna-Gangbo-Subía and others. 1 The main result In the present article we discuss the following minimization problem α (p, q, r) = inf ( kukp kukq : u ∈W 1,p per (−1, 1) \ {0} , Z...
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ژورنال
عنوان ژورنال: Archivum Mathematicum
سال: 2013
ISSN: 0044-8753,1212-5059
DOI: 10.5817/am2013-1-35