scholarly journals On bounded solutions of exterior boundary value problems for linear and quasilinear elliptic differential equations

1965 ◽  
Vol 35 (0) ◽  
pp. 31-59 ◽  
Author(s):  
Takasi KUSANO
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Bounded Solutions ◽  
Exterior Boundary ◽  
Elliptic Differential Equations ◽  
Quasilinear Elliptic

Existence of bounded solutions of integral boundary value problems for singular differential equations on whole lines

2014 ◽  
Vol 25 (08) ◽  
pp. 1450078 ◽  
Author(s):  
Yuji Liu ◽  
Shengping Chen
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Nonlinear Operator ◽  
Boundary Value ◽  
Nonnegative Function ◽  
Bounded Solutions ◽  
Integral Boundary ◽  
Singular Differential Equations ◽  
Nonlinear Alternative ◽  
Integral Boundary Value Problems

Boundary value problems of second-order singular differential equations with nonlinear operator Φ on whole lines are discussed. By applying the nonlinear alternative of Leray–Schauder-type fixed point theorem, some existence results of solutions for integral boundary value problems of differential equations on whole lines are established. The emphasis is put on the nonlinear operator [Φ(ρ(t)x′(t))]′ involved with the nonnegative function ρ that may satisfy ρ(0) = 0, the strictly increasing sup-multiplicative-like function Φ and the differential equations are defined on the whole line. Three examples and a remark are presented to illustrate the main theorems.

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