Landesman-Lazer Type Condition Research Articles

ON A NEUMANN PROBLEM AT RESONANCE FOR NONUNIFORMLY SEMILINEAR ELLIPTIC SYSTEMS IN AN UNBOUNDED DOMAIN WITH NONLINEAR BOUNDARY CONDITION

We consider a nonuniformly nonlinear elliptic systems with resonance part and nonlinear Neumann boundary condition on an unbounded domain. Our arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type condition.

Asymptotically linear systems near and at resonance

This paper deals with an elliptic system of the form in Ω, in Ω, on ∂ Ω, where is a parameter and ( ) is a bounded domain with -boundary ∂ Ω, (a bounded open interval if ). Here with a.e. in Ω and are constants. The nonlinear perturbations are Caratheodory functions that are sublinear at infinity. We provide sufficient conditions for determining the λ-direction to which a continuum of positive and negative solutions emanates from infinity at the first eigenvalue of the associated linear problem. Furthermore, as a consequence of main results, we also provide sufficient condition for the solvability of a class of asymptotically linear system near and at resonance satisfying Landesman-Lazer type conditions. MSC: 35J60.

An asymmetric superlinear elliptic problem at resonance

In this article, we study the existence and multiplicity of solutions to the problem {−Δu=g(x,u), in Ω;u=0, on ∂Ω, where Ω is a bounded domain in RN(N⩾2) with smooth boundary, and g:Ω¯×R→R is a differentiable function. We will assume that g(x,s) has a resonant behavior for large negative values of s and that a Landesman–Lazer type condition is satisfied. We also assume that g(x,s) is superlinear, but subcritical, for large positive values of s. We prove the existence and multiplicity of solutions for problem (1.1) by using minimax methods and infinite-dimensional Morse theory.

A Landesman-Lazer type condition for second-order differential equations with a singularity at resonance

In this paper, we are concerned with the existence of positive periodic solutions for second-order differential equations with a singularity at resonance. A Landesman-Lazer type condition is given to obtain the existence of positive periodic solutions using phase-plane analysis method and topological degree method.

RETRACTED ARTICLE: Landesman-Lazer type condition for second-order differential equations at resonance with impulsive effects

In this paper, we study the existence of periodic solutions of second-order impulsive differential equations at resonance. We prove the existence of periodic solutions under a generalized Landesman-Lazer type condition by using the variational method. The impulses can generate a periodic solution.

Bounded solutions for a forced bounded oscillator without friction

Under the validity of a Landesman–Lazer type condition, we prove the existence of solutions bounded on the real line, together with their first derivatives, for some second order nonlinear differential equation of the form u¨+g(u)=p(t), where the reaction term g is bounded. The proof is variational, and relies on a dual version of the Nehari method for the existence of oscillating solutions to superlinear equations.

Landesman-lazer type conditions and multiplicity results for nonlinear elliptic problems with neumann boundary values

We establish the existence and multiplicity of solutions for Steklov problems under nonresonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.

Resonance with respect to the Fučík spectrum for non-selfadjoint operators

In this paper, we consider a real linear (non-selfadjoint) operator L:Dom(L)⊂L2(Ω)→L2(Ω) and study the solvability of the problem Lu−αu++βu−−g(u)+f=0 in the resonance case with respect to the Fučík spectrum Σ(L). We extend the standard Landesman–Lazer type conditions and compare our result with results for selfadjoint operators as well as with results for the resonance in the point spectrum (i.e., for α=β∈σ(L)).

Resonance problems for Kirchhoff type equations

The existence of weak solutions is obtained for some Kirchhoff typeequations with Dirichlet boundary conditions which are resonant atan arbitrary eigenvalue under a Landesman-Lazer type condition bythe minimax methods.

A Landesman–Lazer-type condition for asymptotically linear second-order equations with a singularity

We consider the T-periodic problemwhere g: [0,T]×]0,+∞[→ℝ exhibits a singularity of a repulsive type at the origin, and an asymptotically linear behaviour at infinity. In particular, for large x, g(t, x) is controlled from both sides by two consecutive asymptotes of the T-periodic Fučik spectrum, with possible equality on one side. Using a suitable Landesman–Lazer-type condition, we prove the existence of a solution.

Periodic solutions for nonlinear evolution equations at resonance

We are concerned with periodic problems for nonlinear evolution equations at resonance of the form u˙(t)=−Au(t)+F(t,u(t)), where a densely defined linear operator A:D(A)→X on a Banach space X is such that −A generates a compact C0 semigroup and F:[0,+∞)×X→X is a nonlinear perturbation. Imposing appropriate Landesman–Lazer type conditions on the nonlinear term F, we prove a formula expressing the fixed point index of the associated translation along trajectories operator, in the terms of a time averaging of F restricted to KerA. By the formula, we show that the translation operator has a nonzero fixed point index and, in consequence, we conclude that the equation admits a periodic solution.

Existence and multiplicity of solutions for asymptotically linear noncooperative elliptic systems

Using the minimax methods in critical point theory and a generalized Landesman–Lazer type condition, we establish two existence results of solutions for asymptotically linear noncooperative elliptic systems at resonance. Besides this, we obtain two solutions in the case of near resonance.

Multiple solutions for semilinear elliptic equations near resonance at higher eigenvalues

Using the minimax methods in critical point theory and a generalized Landesman–Lazer type condition, we obtain two solutions for a class of semilinear elliptic equations near resonance at higher eigenvalues.

Forced Duffing Equation With a Resonance Condition

Abstract This article is devoted to the study of the existence of a solution to the periodic nonlinear second order ordinary differential equation with damping uʺ (x) + cuʹ (x) + g(x,u(x)) = f(x), x ∈ [0, T], u(0) = u(T), uʹ(0) = uʹ(T), where c ∈ ℝ, g is a Caratheodory function, f ∈ L1([0, T), a quotient lies between 0 and and a nonlinearity g satisfies Landesman Lazer type condition near the zero. The techniques we use are a variational method and a critical point theorem.

Resonance problems for the p-Laplacian systems

Two existence theorems of the solutions are obtained for the p-Laplacian systems at resonance under a Landesman–Lazer-type condition by critical point theory.

Nagumo and Landesman-Lazer type conditions for nonlinear second order systems

We study the existence of solutions for a nonlinear second order system of ordinary differential equations under various boundary conditions. Assuming suitable Nagumo type conditions we prove the existence of at least one solution applying the method of upper and lower solutions. Moreover, using topological degree methods we prove the existence of solutions under Landesman-Lazer type conditions.

Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity

We consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation producing solutions that bifurcate from infinity. We study the bifurcation branches, characterize when they are sub- or supercritical and analyse the stability type of the solutions. Furthermore, we apply these results and techniques to obtain Landesman–Lazer-type conditions guaranteeing the existence of solutions in the resonant case and to obtain an anti-maximum principle.

Landesman–Lazer type conditions for a system of p-Laplacian like operators

We study the existence of periodic solutions for a nonlinear second order system of ordinary differential equations of p-Laplacian type. Assuming suitable Nagumo and Landesman–Lazer type conditions we prove the existence of at least one solution applying topological degree methods. We extend a celebrated result by Nirenberg for resonant systems.

A nonlinear second order problem witha nonlocal boundary condition

We study a nonlinear problem of pendulum‐type for a p‐Laplacian with nonlinear periodic‐type boundary conditions. Using an extension of Mawhin′s continuation theorem for nonlinear operators, we prove the existence of a solution under a Landesman‐Lazer type condition. Moreover, using the method of upper and lower solutions, we generalize a celebrated result by Castro for the classical pendulum equation.

Periodic solutions for second order differential inclusions with the scalar p-Laplacian

We study periodic problems driven by the scalar p-Laplacian with a multivalued right-hand side nonlinearity. We prove two existence theorems. In the first, we assume nonuniform nonresonance conditions between two successive eigenvalues of the negative p-Laplacian with periodic boundary conditions. In the second, we employ certain Landesman–Lazer type conditions. Our approach is based on degree theory.