We study the existence of the weak solution of the nonlinear boundary-value problem −(|u′|p−2u′)′ = λ|u|p−2u+ g(u)− h(x) in (0, π), u(0) = u(π) = 0 , where p and λ are real numbers, p > 1, h ∈ Lp (0, π) (p′ = p p−1 ) and the nonlinearity g : R → R is a continuous function of the Landesman-Lazer type. Our sufficiency conditions generalize the results published previously about the solvability of...

We give an elementary proof of a Landesman-Lazer type result for systems by means shooting argument and explore its connection with the fundamental theorem algebra.

This paper is concerned with the bifurcation from infinity of nonlinear Schrödinger equation ??u+V(x)u=?u+f(x,u),x?RN. We treat this problem in framework dynamical systems by considering corresponding parabolic on unbounded domains. Firstly, we establish a global invariant manifold for RN. Then, restrict to manifold, which generates system finite dimension. Finally, use Conley index theory and ...

The aim of this paper is to establish some a priori bounds for solutions of Landesman-Lazer problem. We show the application for the solution structure of the nonlinear diierential equation of the fourth order 1. The general theory Let X be a real Banach space with the norm k k and let D(L) X be the domain of the closed Fredholm operator L : D(L) ! X with index zero. We shall suppose that 0 is ...

Keywords: Second order differential systems Saddle point theorem Generalized Ahmad–Lazer–Paul type condition a b s t r a c t Existence of periodic solutions to second order differential systems with gyroscopic forces is considered via variational methods, where a generalized Ahmad–Lazer–Paul type condition is used. We do not impose the condition that the gyroscopic forces are small.

We consider the boundary value problem $$\displaylines{ - \Delta u + c(x) = \alpha m(x) u^+ \beta u^- +f(x,u), \quad x \in \Omega, \cr \frac{\partial u}{\partial \eta} \sigma (x) =\alpha \rho u^+- +g(x,u), \partial }$$ where \((\alpha, \beta) \mathbb{R}^2\), \(c, m L^\infty (\Omega)\), \(\sigma, (\partial\Omega)\), and nonlinearities f g are bounded continuous functions. study asymmetric (Fucik...