scholarly journals MULTIPLE SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEMS WITH OSCILLATORY SOLUTIONS

2006 ◽  
Vol 11 (4) ◽  
pp. 413-426 ◽  
Author(s):  
S. Ogorodnikova ◽  
F. Sadyrbaev
Keyword(s):  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Nonlinear Boundary Value Problems ◽  
Number Of Solutions ◽  
Oscillatory Solutions ◽  
Autonomous Differential Equations

We consider two second order autonomous differential equations with critical points, which allow the detection of an exact number of solutions to the Dirichlet boundary value problem. Non‐autonomous equations with similar behaviour of solutions also are considered. Estimations from below of the number of solutions to the Dirichlet boundary value problem are given.

scholarly journals On the existence of multiple solutions for a partial discrete Dirichlet boundary value problem with mean curvature operator

2021 ◽  
Vol 11 (1) ◽  
pp. 198-211
Author(s):  
Sijia Du ◽  
Zhan Zhou
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Mean Curvature ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Curvature Operator ◽  
Dirichlet Boundary Value Problem ◽  
The Maximum Principle ◽  
Mean Curvature Operator

Abstract Apartial discrete Dirichlet boundary value problem involving mean curvature operator is concerned in this paper. Under proper assumptions on the nonlinear term, we obtain some feasible conditions on the existence of multiple solutions by the method of critical point theory. We further separately determine open intervals of the parameter to attain at least two positive solutions and an unbounded sequence of positive solutions with the help of the maximum principle.

scholarly journals ON SOME SPECTRAL PROPERTIES OF THIRD ORDER NONLINEAR BOUNDARY VALUE PROBLEMS

2012 ◽  
Vol 17 (1) ◽  
pp. 78-89 ◽  
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Value Problem ◽  
Spectral Properties ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Third Order ◽  
Number Of Solutions ◽  
Nodal Structure ◽  
The Third ◽  
Nonlinear Boundary Value

The present paper deals with a two point the third-order nonlinear boundary value problem. An estimation of the number of solutions to boundary value problem and their nodal structure are established. Some results are given on spectral properties of solutions.

scholarly journals Existence theory for single and multiple solutions to semipositone discrete Dirichlet boundary value problems with singular dependent nonlinearities

2003 ◽  
Vol 16 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Daqing Jiang ◽  
Lili Zhang ◽  
Donal O'Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Existence Theory ◽  
Dirichlet Boundary Value Problem

In this paper we establish the existence of single and multiple solutions to the semipositone discrete Dirichlet boundary value problem {Δ2y(i−1)+μf(i,y(i))=0,            i∈{1,2,…,T}y(0)=y(T+1)=0, where μ>0 is a constant and our nonlinear term f(i,u) may be singular at u=0.

Singular perturbation of a nonlinear problem with multiple solutions

1985 ◽  
Vol 100 (3-4) ◽  
pp. 327-341
Author(s):  
Anne-Marie Lefevere
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Critical Value ◽  
Free Boundary Value Problem ◽  
Singular Limits ◽  
Natural Extensions ◽  
Barrier Parameter

SynopsisA nonlinear boundary value problem (P) having positive parameters L and a is considered. We associate with it a family of perturbed problems () affected by the presence of a barrier parameter γ related to L and a. There is a critical value L*(a) of the parameter L such that for L >L*(a), (P) has no regular solution. Then some natural extensions of (P), solutions of a free boundary value problem, arise as singular limits of ().

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