scholarly journals ON A METHOD OF INVESTIGATING THE STEKLOV PROBLEM FOR THE 3-DIMENSIONAL LAPLACE EQUATION WITH NON-LOCAL BOUNDARY-VALUE CONDITIONS

2016 ◽  
pp. 19-33
Author(s):  
Yelena Y MUSTAFAYEVA ◽  
◽  
Nehan Ali. ALIEV ◽  
Keyword(s):  
Laplace Equation ◽  
Boundary Value ◽  
Steklov Problem ◽  
Local Boundary ◽  
3 Dimensional ◽  
Non Local

On Semipositone Non-Local Boundary-Value Problems with Nonlinear or Affine Boundary Conditions

2016 ◽  
Vol 60 (3) ◽  
pp. 635-649 ◽  
Author(s):  
Christopher S. Goodrich
Keyword(s):  
Existence Result ◽  
Boundary Value ◽  
Growth Conditions ◽  
Compact Set ◽  
Boundedness Condition ◽  
Local Boundary ◽  
Semipositone Problem ◽  
Non Local ◽  
Image Position ◽  
Special Case

AbstractWe consider the boundary-value problemwhereH: [0,+∞) → ℝ andf: [0, 1] × ℝ → ℝ are continuous and λ > 0 is a parameter. We show that ifHsatisfies a boundedness condition on a specified compact set, then this, together with an assumption thatHis either affine or superlinear at +∞, implies existence of at least one positive solution to the problem, even in the case where we impose no growth conditions onf. Finally, since it can hold thatf(t, y) < 0 for all (t, y) ∈ [0, 1]×ℝ, the semipositone problem is included as a special case of the existence result.

Sign in / Sign up

Export Citation Format

Share Document