Solvability of a nonlinear Sturm-Liouville boundary-value problem for a second-order integrodifferential equation with one-sided restrictions on the growth of the right side with respect to the first derivative

1987 ◽  
Vol 36 (2) ◽  
pp. 292-300
Author(s):  
M. N. Yakovlev
Keyword(s):  
Boundary Value Problem ◽  
Integrodifferential Equation ◽  
Boundary Value ◽  
Second Order ◽  
First Derivative ◽  
Sturm Liouville ◽  
The Right

scholarly journals Multiplicity of positive solutions for second order Sturm-Liouville boundary value problems

2016 ◽  
Vol 25 (2) ◽  
pp. 215-222
Author(s):  
K. R. PRASAD ◽  
◽  
N. SREEDHAR ◽  
L. T. WESEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
Multiplicity Of Positive Solutions

In this paper, we develop criteria for the existence of multiple positive solutions for second order Sturm-Liouville boundary value problem, u 00 + k 2u + f(t, u) = 0, 0 ≤ t ≤ 1, au(0) − bu0 (0) = 0 and cu(1) + du0 (1) = 0, where k ∈ 0, π 2 is a constant, by an application of Avery–Henderson fixed point theorem.

Existence of positive solutions for second-order undamped Sturm–Liouville boundary value problems

2016 ◽  
Vol 09 (04) ◽  
pp. 1650089 ◽  
Author(s):  
K. R. Prasad ◽  
L. T. Wesen ◽  
N. Sreedhar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

In this paper, we consider the second-order differential equations of the form [Formula: see text] satisfying the Sturm–Liouville boundary conditions [Formula: see text] where [Formula: see text]. By an application of Avery–Henderson fixed point theorem, we establish conditions for the existence of multiple positive solutions to the boundary value problem.

scholarly journals Existence principles for second order nonresonant boundary value problems

1994 ◽  
Vol 7 (4) ◽  
pp. 487-507 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Carathéodory Function ◽  
Sturm Liouville

We discuss the two point singular “nonresonant” boundary value problem 1p(py′)′=f(t,y,py′) a.e. on [0,1] with y satisfying Sturm Liouville, Neumann, Periodic or Bohr boundary conditions. Here f is an L1-Carathéodory function and p∈C[0,1]∩C1(0,1) with p>0 on (0,1).

scholarly journals TYPES AND MULTIPLICITY OF SOLUTIONS TO STURM–LIOUVILLE BOUNDARY VALUE PROBLEM

2015 ◽  
Vol 20 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Maria Dobkevich ◽  
Felix Sadyrbaev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Boundary Value Problems ◽  
Multiplicity Of Solutions ◽  
Different Types ◽  
Sturm Liouville

We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.

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