Some nodal properties for a quasilinear differential equation involving the p-Laplacian

2019 ◽  
Vol 472 (1) ◽  
pp. 1093-1105
Author(s):  
Wei-Chuan Wang
Keyword(s):  
Differential Equation ◽  
Quasilinear Differential Equation ◽  
Nodal Properties

scholarly journals Existence and asymptotic behavior of intermediate type of positive solutions of fourth-order nonlinear differential equations

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4185-4211
Author(s):  
Katarina Djordjevic ◽  
Jelena Manojlovic
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Fourth Order ◽  
Asymptotic Form ◽  
Nonlinear Differential Equations ◽  
Quasilinear Differential Equation ◽  
Intermediate Type ◽  
Integral Conditions ◽  
Regularly Varying Functions ◽  
Regularly Varying

Under the assumptions that p and q are regularly varying functions satisfying conditions ??a t/p(t)1/? dt < ? and ??a (t/p(t))1/? dt = ? existence and asymptotic form of regularly varying intermediate solutions are studied for a fourth-order quasilinear differential equation (p(t)jx??(t)|?-1 x??(t))?? + q(t)|x(t)|?-1 x(t) = 0, ? > ? > 0. It is shown that under certain integral conditions there exist two types of intermediate solutions which according to their asymptotic behavior is to be divided into six mutual distinctive classes, while asymptotic behavior of each member of any of these classes is governed by a unique explicit law.

scholarly journals A New Oscillation Criterion for Forced Second-Order Quasilinear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Shao Jing
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Generalized Variational Principle ◽  
Quasilinear Differential Equation ◽  
Riccati Technique ◽  
Forcing Term

By using the generalized variational principle and Riccati technique, a new oscillation criterion is established for second-order quasilinear differential equation with an oscillatory forcing term, which improves and generalizes some of new results in the literature.

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