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On maximum principles for solutions to nonlinear elliptic ODEs and radial solutions to nonlinear elliptic PDE's via Opial‐type inequalities
Author(s) -
Kałamajska Agnieszka,
Maria Kosiorek Anna
Publication year - 2021
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.7055
Subject(s) - mathematics , nonlinear system , type (biology) , monotonic function , elliptic curve , mathematical analysis , a priori and a posteriori , maximum principle , ball (mathematics) , ode , mathematical optimization , physics , quantum mechanics , biology , philosophy , ecology , epistemology , optimal control
We consider degenerated nonlinear PDE of elliptic type:− div ( a ( | x | ) | ∇ w ( x ) |p − 2 ∇ w ( x ) ) + h | x | , w ( x ) , ∇ w ( x ) , x | x |= ϕ ( w ( x ) ) , a.e. in the ball inℝ n . Using the argument based on Opial‐type inequalities, we investigate qualitative properties of their radial solutions, like, for example, the a priori estimates, maximum principles, monotonicity, as well as nonexistence of the nontrivial solutions.