Publication Date:
2015-06-14
Description:
This paper deals with the existence of positive doubly periodic solutions for the nonlinear telegraph equation with delays L u = f ( t , x , u ( t − τ 1 , x ) , … , u ( t − τ n , x ) ) , ( t , x ) ∈ R 2 , where L u : = u t t − u x x + c u t + a ( t , x ) u is a linear telegraph operator acting on function u : R 2 → R , c 〉 0 is a constant, a ∈ C ( R 2 , ( 0 , ∞ ) ) is 2π-periodic in t and x, f ∈ C ( R 2 × [ 0 , ∞ ) n , [ 0 , ∞ ) ) is 2π-periodic in t and x, and τ 1 , … , τ n ∈ [ 0 , ∞ ) are constants. Some existence results of positive doubly 2π-periodic weak solutions are obtained under that f ( t , x , η 1 , … , η n ) satisfies some superlinear or sublinear growth conditions on η 1 , … , η n . The discussion is based on the fixed point index theory in cones.MSC: 35B15, 47H10.
Print ISSN:
1687-2762
Electronic ISSN:
1687-2770
Topics:
Mathematics
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