New results of periodic solutions for Rayleigh type -Laplacian equation with a variable coefficient ahead of the nonlinear term

2009 ◽  
Vol 70 (5) ◽  
pp. 2072-2077 ◽  
Author(s):  
Liang Feng ◽  
Guo Lixiang ◽  
Shiping Lu
Keyword(s):  
Periodic Solutions ◽  
Variable Coefficient ◽  
Nonlinear Term ◽  
Laplacian Equation

SIGN-CHANGING SOLUTIONS FOR AN ASYMPTOTICALLY p-LINEAR p-LAPLACIAN EQUATION IN ℝN

2013 ◽  
Vol 15 (01) ◽  
pp. 1250046 ◽  
Author(s):  
XIANGQING LIU ◽  
YUXIA GUO
Keyword(s):  
Nonlinear Term ◽  
Positive Parameter ◽  
Laplacian Equation ◽  
Sign Changing Solutions

In this paper, we study the existence of sign-changing solutions for the p-Laplacian equation [Formula: see text] where λ is a positive parameter and the nonlinear term f is superlinear at zero and asymptotically p-linear at infinity.

Existence and Multiplicity of Periodic Solutions to Indefinite Singular Equations Having a Non-monotone Term with Two Singularities

2019 ◽  
Vol 19 (2) ◽  
pp. 317-332 ◽  
Author(s):  
Robert Hakl ◽  
Manuel Zamora
Keyword(s):  
Magnetic Field ◽  
Periodic Solutions ◽  
Nonlinear Term ◽  
Order Differential Equation ◽  
Positive Function ◽  
Periodic Motions ◽  
Formula One ◽  
Existence And Multiplicity ◽  
Oscillating Magnetic Field ◽  
General Sign

AbstractEfficient conditions guaranteeing the existence and multiplicity of T-periodic solutions to the second order differential equation {u^{\prime\prime}=h(t)g(u)} are established. Here, {g\colon(A,B)\to(0,+\infty)} is a positive function with two singularities, and {h\in L(\mathbb{R}/T\mathbb{Z})} is a general sign-changing function. The obtained results have a form of relation between multiplicities of zeros of the weight function h and orders of singularities of the nonlinear term. Our results have applications in a physical model, where from the equation {u^{\prime\prime}=\frac{h(t)}{\sin^{2}u}} one can study the existence and multiplicity of periodic motions of a charged particle in an oscillating magnetic field on the sphere. The approach is based on the classical properties of the Leray–Schauder degree.

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