We study the existence and multiplicity of solutions for nonlocalperturbed Kirchhoff problem$$\displaylines{-\Big(a+b\int_\Omega |\nabla u|^2\,dx\Big)\Delta u=\lambda g(x,u)+f(x,u), \quad \text{in } \Omega,\\ u=0, \quad\text{on }\partial\Omega,}$$ where Ω is a bounded smooth domain in \(\mathbb{R}^N\), \(N>4\), \(a,b, \lambda > 0\), \(f,g:\Omega\times \mathbb{R}\to \mathbb{R}\) ...

Let a smooth manifold M be equipped with a smoothly varying positive definite quadratic form on a distribution-subbundle V of the tangent bundle TM. One assumes that V is completely nonintegrable, equivalently all sections of V together with all brackets between them generate TM at each point of M. Then by the well-known theorem of Rashevski-Chow [3] it is possible to connect any two points (in...

In this article we investigate the existence of extremal(maximal and minimal) solutions for the following coupled system of integrodifferential equations of fractional order with the given boundary conditions of the form  Du(t) + f1(t, v(t), I v(t)) = 0, 0 < t < 1, Dv(t) + f2(t, u(t), I u(t)) = 0, 0 < t < 1, u(0) = 0, u′(1) = 0, v(0) = 0, v′(1) = 0. where 1 < α, β ≤ 2 and f1, f2 : [0, 1] × ...

We develop monotone iterative technique for a system of semilinear elliptic boundary value problems when the forcing function is the sum of Caratheodory functions which are nondecreasing and nonincreasing, respectively. The splitting of the forcing function leads to four different types of coupled weak upper and lower solutions. In this paper, relative to two of these coupled upper and lower so...