[PDF] Top 20 Periodic solutions of radially symmetric systems with a singularity

... dynamical systems in the liter- ature, including the degree theory [–], the method of upper and lower solutions [, ], Schauder’s fixed point theorem [–], some fixed point theorems in cones for ... See full document

... of periodic solutions for second order differential equations with ...the singularity has a significant background in applied sciences and physics (see [–] and the references ...the periodic ... See full document

... of periodic solutions to scalar equations with a singularity began with work of Forbat and Huaux [, ], where the singular term in the equations models the restoring force caused by a compressed ... See full document

... positive periodic solutions to ...(weak singularity condition), some equations like ...the periodic problem for some second-order differential equations with singularities of repulsive type ... See full document

... of periodic solutions for the second order differential equations with a singularity, especially for the Liénard equa- ...of periodic solutions of the Liénard equations with a deviating ... See full document

... positive periodic solutions for equation ...lower solutions methods used in [20, 21], and continuation theorems of coincidence degree used in ...the periodic problem for the equation with ... See full document

... strong singularity, the energy near the ori- gin becomes infinite and this fact is helpful for obtaining either a priori bounds, which are needed for a classical application of the degree theory, or the fast ... See full document

... positive periodic solutions of a kind of p-Laplacian neutral differential equation with a ...positive periodic solutions for the considered ... See full document

... positive periodic solutions for the prescribed mean curvature equation with a singularity is relatively ...the singularity and the nonlinear term ( √ u ... See full document

... function. Obviously, equation (.) and equation (.) are all singular at x = . The first- order derivative term f (x)x in equation (.) and equation (.) satisfies  T f (x(t))x (t) dt = , which is crucial for ... See full document

... (see [] and the references therein). The interest in studying the equations with a singular- ity began with some work of Forbat and Huaux []. Later, the interest in such problem was renewed by Gordon in [, ], and ... See full document

... systems and equation of the type (.), respectively, and obtained some sufficient condi- tions for the existence of infinitely many radial positive entire solutions with the prescribed asymptotic behavior at ... See full document

... Brown, KJ, Castro, A, Shivaji, R: Nonexistence of radially symmetric nonnegative solutions for a class of semi-positone problems. Ko, E, Lee, EK, Shivaji, R: Multiplicity results for cla[r] ... See full document

... A system of coupled nonlinear oscillators is capable of displaying a rich dynamics and has applications in various areas of science and technology, such as physical, chemical, bio- logical, and other systems ... See full document

... Remark 5.4. Observe that if a positively flow-invariant compact ENR-set A ⊂ R n satisfies χ(A) ∈ { 0, 1 } and its boundary ∂A is fixed point free (e.g., if the sharp inequality holds in (5.1)), then at least two ... See full document

... 9. Fadell, E, Husseini, S: A note on the category of free loop space. Proc. Am. Math. Soc. 102, 527-536 (1989) 10. Gordon, WB: Conservative dynamical systems involving strong forces. Trans. Am. Math. Soc. 204, ... See full document

... of solutions in the phase plane of the autonomous ...specific solutions of the autonomous equation give rise to the existence of several new families of singular solutions of the w ...singular ... See full document

... With periodic potentials, that is, (2) holding with r=N, the existence and multiplicity theorems are obtained for the nonautonomous second-order system (1) in [1] and [2] ...partially periodic (that ... See full document

... of periodic and subharmonic solutions for subquadratic first- order (see [1–3]) or second-order (see [4–8]) continuous Hamiltonian systems by using the critical point ... See full document

... To prove our results we adapt Mawhin’s continuation theorem in [2], and we give appropriate region for the system’s multiplicity by finding an a’priori bound.. To prove our assertion, we[r] ... See full document