Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions

Abstract In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

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Existence and multiplicity results for fractional differential inclusions with Dirichlet boundary conditions

Applied Mathematics and Computation ◽

10.1016/j.amc.2012.08.050 ◽

2013 ◽

Vol 220 ◽

pp. 792-801 ◽

Cited By ~ 8

Author(s):

Kaimin Teng ◽

Hongen Jia ◽

Haifeng Zhang

Keyword(s):

Boundary Conditions ◽

Differential Inclusions ◽

Dirichlet Boundary ◽

Dirichlet Boundary Conditions ◽

Fractional Differential Inclusions ◽

Multiplicity Results ◽

Existence And Multiplicity ◽

Fractional Differential

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Multiplicity Results for a Class of Asymptotically Linear Elliptic Problems With Resonance and Applications to Problems With Measure Data

Advanced Nonlinear Studies ◽

10.1515/ans-2010-0210 ◽

2010 ◽

Vol 10 (2) ◽

Cited By ~ 1

Author(s):

Alberto Ferrero ◽

Claudio Saccon

Keyword(s):

Boundary Conditions ◽

Bounded Domain ◽

Dirichlet Boundary ◽

Elliptic Problems ◽

Dirichlet Boundary Conditions ◽

Measure Data ◽

Dirichlet Problems ◽

Asymptotically Linear ◽

Multiplicity Results ◽

Existence And Multiplicity

AbstractWe study existence and multiplicity results for solutions of elliptic problems of the type -Δu = g(x; u) in a bounded domain Ω with Dirichlet boundary conditions. The function g(x; s) is asymptotically linear as |s| → +∞. Also resonant situations are allowed. We also prove some perturbation results for Dirichlet problems of the type -Δu = g

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Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System

International Journal of Differential Equations ◽

10.1155/2016/5676217 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

A. Gritsans ◽

F. Sadyrbaev ◽

I. Yermachenko

Keyword(s):

Vector Field ◽

Dirichlet Boundary ◽

Second Order ◽

Dirichlet Boundary Conditions ◽

Order System ◽

Dirichlet Boundary Value Problem ◽

Asymptotically Linear ◽

Multiplicity Results ◽

Existence And Multiplicity ◽

Field Rotation

We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.

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Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas ◽

10.1007/s13398-021-01080-w ◽

2021 ◽

Vol 115 (3) ◽

Author(s):

Robert Stegliński

Keyword(s):

Difference Equation ◽

Boundary Conditions ◽

Difference Equations ◽

Periodic Boundary ◽

Periodic Boundary Conditions ◽

Second Order ◽

Linear Difference Equations ◽

Order Difference ◽

Second Order Difference Equation ◽

Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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