[PDF] Top 20 Existence of positive periodic solutions for Liénard equations with an indefinite singularity of attractive type

... differential equations with singularities have a wide range of applica- tions in physics, mechanics, and biology ...the equations with singularities ...of periodic problem to second-order differential ... See full document

... a positive and decreasing function which has a strong singularity at the ori- gin, and the weight h ∈ L(R/TZ) is a sign-changing ...the existence of a T- periodic solution to the above ... See full document

... Nowadays, the prescribed mean curvature equation and its modified forms, which arise from some problems associated with differential geometry and physics such as com- bustible gas dynamics, have been studied widely (see ... See full document

... the existence of positive periodic solutions for some types of differential equations with a singularity have been obtained; see [–] and the references cited ...the ... See full document

... the existence of pe- riodic solutions by using topological degree ...the existence of positive periodic solutions of ...repulsive type and attractive ... See full document

... the existence of periodic solutions for Liénard type differential equa- tions was extensively studied (see [–] and the references ...a Liénard type differential equation ... See full document

... The structure of the paper is as follows. Section  contains the tools needed in the proofs. In Section , we state and prove the main results and develop some corollaries for the equation with a singularity of ... See full document

... Newtonian type forces or to restor- ing forces caused by compressed ...the existence of a positive periodic solution is that e ¯ := T   T e(s) ds < ...the existence of ... See full document

... As is well known, the Rayleigh equation can be derived from many fields, such as physics, mechanics and engineering technique fields, and an important question is whether this equation can support periodic ... See full document

... to equations with repulsive singularity or equations with time-independent deviating ...with attractive singularity works on time-dependent deviating argument? Besides practical ... See full document

... The structure of the paper is as follows. After the introduction and basic notation, we recall the definition of lower and upper functions to the problem (.), (.), and we for- mulate the classical theorem on the ... See full document

... where g(x) is singular at x = 0, ϕ and h are T-periodic functions. By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is ... See full document

... differential equations was paid to investigating the problem of periodic solutions for second order differential equations with ...the singularity has a significant background in applied ... See full document

... Theorem 4.6, γ(t) is a homoclinic. The second case shows that γ(t) is a part of a heteroclinic. If the second case occurs, then each solution of (5.20), which lies in heteroclinic, is bounded. By the Poincaré-Bendixon ... See full document

... the existence of positive periodic solutions for second-order dynamic equations on time ...of positive periodic solutions is also ... See full document

... In recent years, the existence of periodic solutions for second-order Li´enard equations u + f (u,u )u + g (u) = e(t,u,u ) (1.1) and its special case have been studied by many researchers, we ... See full document

... are periodic functions of period ω and τ >0 is a fixed real ...has periodic solutions if and only if (1) holds for all periodic solutions y(t) of period ω of the adjoint ... See full document

... weak singularity can play an important role if Schauder’s fixed point theorem is chosen in the proof of the existence of positive periodic solutions for ...is positive in a set of ... See full document

... the periodic solutions for p−Laplacian differential equation with singular forces of attractive ...the existence of periodic solutions are ... See full document

... the existence of periodic solutions for the p-Laplacian equation (see [–] and refer- ences therein), studying delay Liénard equations with a variable coefficient in front of the ... See full document