Optimal conditions of solvability of nonlocal problems for second-order ordinary differential equations

For the differential equation

u^″=f(t,u)     

Periodic solutions for a higher order p-Laplacian neutral functional differential equation with a deviating argument

In this paper, a higher order p-Laplacian neutral functional differential equation with a deviating argument:

[φ_p([x(t)−c(t)x(t−σ)]⁽ⁿ⁾)]^(m)+f(x(t))x^′(t)+g(t,x(t−τ(t)))=e(t)     

Nonhomogeneous boundary value problems for some nonlinear equations with singular ?-Laplacian

Using Leray-Schauder degree theory we obtain various existence results for the quasilinear equation problems

(?(u^′)^)′=f(t,u,u^′)     

Periodic solutions of some second-order differential equations with desultorily sublinear nonlinearities

In this paper, we study the existence of periodic solutions of the Rayleigh equations

x^″+f(x^′)+g(x)=e(t).     

Existence result for a third-order ODE with nonlinear boundary conditions in presence of a sign-type Nagumo control

In this work we provide an existence and location result for the third-order nonlinear differential equation

u^?(t)=f(t,u(t),u^′(t),u^″(t)),     

On the distribution of zeros of solutions of first order delay differential equations

This paper contains new estimates for the distance between adjacent zeros of solutions of the first order delay differential equation

x^′(t)+p(t)x(t−τ)=0     

Existence, uniqueness and stability of travelling waves in a discrete reaction-diffusion monostable equation with delay

In this paper, we study the existence, uniqueness and asymptotic stability of travelling wavefronts of the following equation:

u_t(x,t)=D[u(x+1,t)+u(x-1,t)-2u(x,t)]-du(x,t)+b(u(x,t-r)),     

On a nonlinear eigenvalue problem in ODE

In this paper we shall study the following variant of the logistic equation with diffusion:

−du^″(x)=g(x)u(x)−u²(x)     

The geometry of the critical set of nonlinear periodic Sturm-Liouville operators

We study the critical set C of the nonlinear differential operator F(u)=−u^″+f(u) defined on a Sobolev space of periodic functions Hp(S¹), p?1. Let be the plane z=0 and, for n>0, let n be the cone x²+y²=tan²z, |z−2πn|<π/2; also set . For a generic smooth nonlinearity f:R→R with surjective derivative, we show that there is a diffeomorphism between the pairs (Hp(S¹),C) and (R³,Σ)×H where H is a real separable infinite-dimensional Hilbert space.     

Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations

We study the convergence and decay rate to equilibrium of bounded solutions of the quasilinear parabolic equation

ut−diva(x,∇u)+f(x,u)=0     

On some third order nonlinear boundary value problems: Existence, location and multiplicity results

We prove an Ambrosetti-Prodi type result for the third order fully nonlinear equation

u^?(t)+f(t,u(t),u^′(t),u^″(t))=sp(t)     

Study of the solutions to a model porous medium equation with variable exponent of nonlinearity

The authors of this paper study the Dirichlet problem of the following equation

ut−div(|u|^ν(x,t)∇u)=f−|u|^p(x,t)−1u.