Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations

1980 ◽  
Vol 61 (1) ◽  
pp. 67-79 ◽  
Author(s):  
Neil S. Trudinger
Keyword(s):  
Second Order ◽  
Quasilinear Equations ◽  
Subsolutions And Supersolutions

Nonlocal and Initial Problems for Quasilinear, Nonstrictly Hyperbolic Equations with General Solutions Represented by Superposition of Arbitrary Functions

2003 ◽  
Vol 10 (4) ◽  
pp. 687-707
Author(s):  
J. Gvazava
Keyword(s):  
Cauchy Problem ◽  
General Solution ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Quasilinear Equations ◽  
General Solutions ◽  
Parabolic Degeneracy

Abstract We have selected a class of hyperbolic quasilinear equations of second order, admitting parabolic degeneracy by the following criterion: they have a general solution represented by superposition of two arbitrary functions. For equations of this class we consider the initial Cauchy problem and nonlocal characteristic problems for which sufficient conditions are established for the solution solvability and uniquness; the domains of solution definition are described.

scholarly journals Parametrically Excited Oscillations of Second-Order Functional Differential Equations and Application to Duffing Equations with Time Delay Feedback

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Mervan Pašić
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Oscillatory Behaviour ◽  
Quasilinear Equations ◽  
Open Questions ◽  
Control Gain ◽  
Main Equation ◽  
Functional Differential ◽  
Time Delayed Feedback

We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.

Oscillation Criteria for Quasilinear Equations

1974 ◽  
Vol 26 (4) ◽  
pp. 931-947 ◽  
Author(s):  
W. Allegretto
Keyword(s):  
Elliptic Equation ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Quasilinear Equations ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Second Order Elliptic Equation

Several authors have recently considered the problem of establishing sufficient criteria to guarantee the oscillation or non-oscillation of all solutions of a second order elliptic equation or system. We mention in particular the papers of C. A. Swanson, [15; 16], K. Kreith [9], Kreith and Travis [10], Noussair and Swanson [13], Allegretto and Swanson [3], Allegretto and Erbe [2] and the references therein.

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