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Some regularity results to the generalized Emden–Fowler equation with irregular data
Author(s) -
Kałamajska Agnieszka,
Mazowiecka Katarzyna
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3235
Subject(s) - mathematics , a priori and a posteriori , multiplicative function , nonlinear system , order (exchange) , boundary (topology) , inequality , mathematical analysis , calculus (dental) , pure mathematics , medicine , philosophy , physics , dentistry , epistemology , finance , quantum mechanics , economics
We deal with the generalized Emden–Fowler equation f ″ ( x ) + g ( x ) f − θ ( x ) = 0, where θ ∈ R , x ∈ ( a , b ) , g belongs to L p (( a , b )). We obtain a priori estimates for the solutions, as well as information about their asymptotic behavior near boundary points. As a tool, we derive new nonlinear variants of first‐order and second‐order Poincaré inequalities, which are based on strongly nonlinear multiplicative inequalities obtained recently by first author and Peszek. Copyright © 2014 John Wiley & Sons, Ltd.