Existence for a semilinear sixth-order ODE

Existence and nonexistence of nontrivial solutions of semilinear sixth-order ordinary differential equations

K e y w o r d s E x t e n d e d Fisher-Kolmogorov equation, Sixth-order equations, Eigenvalue problems~ Clark's theorem, Variational methods. 1. I N T R O D U C T I O N Bistable systems play an important role in the study of spatial patterns. Recently, interest has turned to higher-order model equations involving bistable dynamics, such as the extended Fisher-Kolmogorov (EFK) equation Ou 0% 02u...

Existence and Multiplicity of Positive Solutions of a Boundary-Value Problem for Sixth-Order ODE with Three Parameters

We study the existence and multiplicity of positive solutions of the following boundary-value problem: −u 6 − γu 4 βu − αu ft, u, 0 < t < 1, u0 u1 u 0 u 1 u 4 0 u 4 1 0, where f : 0, 1× R → R is continuous, α, β, and γ ∈ R satisfy some suitable assumptions.

Existence and nonexistence of positive solution for sixth-order boundary value problems

‎In this paper‎, ‎we formulate the sixth-order boundary value problem as Fredholm integral equation by finding Green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problem‎. ‎Also nonexistence results are obtained‎. ‎An example is given to illustrate the results of paper‎.

Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

A Boundary Va Lue Problem for a Semilinear Second Order Ode