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Displaying similar documents to “Resonance and multiplicity in periodic boundary value problems with singularity”

Periodic BVP with φ -Laplacian and impulses

Vladimír Polášek (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The paper deals with the impulsive boundary value problem d d t [ φ ( y ' ( t ) ) ] = f ( t , y ( t ) , y ' ( t ) ) , y ( 0 ) = y ( T ) , y ' ( 0 ) = y ' ( T ) , y ( t i + ) = J i ( y ( t i ) ) , y ' ( t i + ) = M i ( y ' ( t i ) ) , i = 1 , ... m . The method of lower and upper solutions is directly applied to obtain the results for this problems whose right-hand sides either fulfil conditions of the sign type or satisfy one-sided growth conditions.

On a two-point boundary value problem for second order singular equations

Alexander Lomtatidze, P. Torres (2003)

Czechoslovak Mathematical Journal

Similarity:

The problem on the existence of a positive in the interval ] a , b [ solution of the boundary value problem u ' ' = f ( t , u ) + g ( t , u ) u ' ; u ( a + ) = 0 , u ( b - ) = 0 is considered, where the functions f and g ] a , b [ × ] 0 , + ∞ [ → ℝ satisfy the local Carathéodory conditions. The possibility for the functions f and g to have singularities in the first argument (for t = a and t = b ) and in the phase variable (for u = 0 ) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established.