Recent topics on nonlinear partial differential equations: Structure of radial solutions for semilinear elliptic equations

2003 ◽  
pp. 121-137
Author(s):  
Eiji Yanagida ◽  
Shoji Yotsutani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Equations ◽  
Nonlinear Partial Differential Equations ◽  
Semilinear Elliptic Equations ◽  
Radial Solutions ◽  
Partial Differential ◽  
Semilinear Elliptic

scholarly journals On the Cauchy problem for semilinear elliptic equations

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Nguyen Huy Tuan ◽  
Tran Thanh Binh ◽  
Tran Quoc Viet ◽  
Daniel Lesnic
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Elliptic Equations ◽  
Elliptic Partial Differential Equations ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
The Cauchy Problem ◽  
Ill Posed

AbstractWe study the Cauchy problem for nonlinear (semilinear) elliptic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak

scholarly journals Positive and oscillatory radial solutions of semilinear elliptic equations

1997 ◽  
Vol 10 (1) ◽  
pp. 95-108 ◽  
Author(s):  
Shaohua Chen ◽  
William R. Derrick ◽  
Joseph A. Cima
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Elliptic Equations ◽  
Nonlinear Partial Differential Equation ◽  
Semilinear Elliptic Equations ◽  
Radial Solutions ◽  
Partial Differential ◽  
Semilinear Elliptic ◽  
Positive Radial Solutions

We prove that the nonlinear partial differential equation Δu+f(u)+g(|x|,u)=0, in  ℝn,n≥3, with u(0)>0, where f and g are continuous, f(u)>0 and g(|x|,u)>0 for u>0, and limu→0+f(u)uq=B>0, for 1<q<n/(n−2), has no positive or eventually positive radial solutions. For g(|x|,u)≡0, when n/(n−2)≤q<(n+2)/(n−2) the same conclusion holds provided 2F(u)≥(1−2/n)uf(u), where F(u)=∫0uf(s)ds. We also discuss the behavior of the radial solutions for f(u)=u3+u5 and f(u)=u4+u5 in ℝ3 when g(|x|,u)≡0.

Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Nonlinear Partial Differential Equations ◽  
Dirichlet Boundary Conditions ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Lyapunov Inequalities ◽  
Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

scholarly journals Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 545-554
Author(s):  
Asghar Ali ◽  
Aly R. Seadawy ◽  
Dumitru Baleanu
Keyword(s):  
Wave Propagation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Longitudinal Wave ◽  
Symbolic Computation ◽  
Boussinesq Equation ◽  
Nonlinear Partial Differential Equations ◽  
Wave Model ◽  
Simple Equation ◽  
Partial Differential

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{&#x03A8;}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.

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