Search results for "Point boundary"

A geometrical criterion for nonexistence of constant-sign solutions for some third-order two-point boundary value problems

2020

We give a simple geometrical criterion for the nonexistence of constant-sign solutions for a certain type of third-order two-point boundary value problem in terms of the behavior of nonlinearity in the equation. We also provide examples to illustrate the applicability of our results.

Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance

2007

Abstract Estimations of the number of solutions are given for various resonant cases of the boundary value problem 𝑥″ + 𝑔(𝑡, 𝑥) = 𝑓(𝑡, 𝑥, 𝑥′), 𝑥(𝑎) cos α – 𝑥′(𝑎) sin α = 0, 𝑥(𝑏) cos β – 𝑥′(𝑏) sin β = 0, where 𝑔(𝑡, 𝑥) is an asymptotically linear nonlinearity, and 𝑓 is a sublinear one. We assume that there exists at least one solution to the BVP.

A Mountain Pass Theorem for a Suitable Class of Functions

2009

Explicit solutions of two-point boundary value operator problems

1988

Soit H un espace de Hilbert, complexe, separable et soit L(H) l'algebre de tous les operateurs lineaires bornes sur H. On etudie des conditions d'existence non triviales pour le probleme aux valeurs limites operateurs: t 2 X (2) +tA 1 X (1) +A 0 X=0; M 11 X(a)+N 11 X(b)+M 12 X (1) (a)+N 12 X (1) (b)=0, M 21 X(a)+N 21 X(b)+M 22 X (1) (a)+N 22 X (1) (b)=0, 0<a≤t≤b ou M ij , N ij , pour 1≤i, j≤2 et A 0 , A 1 sont des operateurs de L(H). Sous certaines hypotheses concernant l'existence des solutions d'une equation operateur algebrique X 2 +B 1 X+B 0 =0, on obtient des solutions explicites au probleme aux limites

Existence of three solutions for a quasilinear two point boundary value problem

2002

In this paper we deal with the existence of at least three classical solutions for the following ordinary Dirichlet problem:¶¶ $ \left\{\begin{array}{ll} u'' + \lambda h(u')f(t,\:u) = 0\\ u(0) = u(1) = 0.\\\end{array}\right.\ $ ¶¶Our main tool is a recent three critical points theorem of B. Ricceri ([10]).

Lusternik-Schnirelmann Critical Values and Bifurcation Problems

1987

We present a method to calculate bifurcation branches for nonlinear two point boundary value problems of the following type $$ \{ _{u(a) = u(b) = 0,}^{ - u'' = \lambda G'(u)} $$ (1.1) where G : R → R is a smooth mapping. This problem can be formulated equivalently as $$ g' \left(u \right)= \mu u, $$ (1.2) where $$ g \left(u \right)= \overset{b} {\underset{a} {\int}} G \left(u \left(t \right) \right) dt $$ (1.3) and μ = 1/λ. Solutions of this problem can be found by locating the critical points of the functional g : H → R on the spheres \(S_r= \lbrace x \in H \mid \;\parallel x \parallel =r \rbrace, r >0.\) (The Lagrange multiplier theorem.)

Multiplicity results for fourth order two-point boundary value problems with asymmetric nonlinearities

1998

On the numerical solution of the distributed parameter identification problem

1991

A new error estimate is derived for the numerical identification of a distributed parameter a(x) in a two point boundary value problem, for the case that the finite element method and the fit-to-data output-least-squares technique are used for the identifications. With a special weighted norm, we get a pointwise estimate. Prom the error estimate and also from the numerical tests, we find that if we decrease the mesh size, the maximum error between the identified parameter and the true parameter will increase. In order to improve the accuracy, higher order finite element spaces should be used in the approximations.

Green’s function and existence of solutions for a third-order three-point boundary value problem

2019

The solutions of third-order three-point boundary value problem x‘‘‘ + f(t, x) = 0, t ∈ [a, b], x(a) = x‘(a) = 0, x(b) = kx(η), where η ∈ (a, b), k ∈ R, f ∈ C([a, b] × R, R) and f(t, 0) ≠ 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green’s function. As an application, also one example is given to illustrate the result. Keywords: Green’s function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.

AN APPLICATION OF A FIXED POINT THEOREM FOR NONEXPANSIVE OPERATORS

2014

Abstract. In this note, we present an application of a recent xed point theorem by Ricceri to a two-point boundary value problem. KeyWords and Phrases: Fixed point, nonexpansive operator, two-point boundary value problem. 2010 Mathematics Subject Classi cation: 34K10, 47H09, 47H10.