Displaying similar documents to “On the existence of multiple periodic solutions for the vector p -Laplacian via critical point theory”

Unique solvability of a linear problem with perturbed periodic boundary values

Bahman Mehri, Mohammad H. Nojumi (1999)

Czechoslovak Mathematical Journal

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We investigate the problem with perturbed periodic boundary values y ' ' ' ( x ) + a 2 ( x ) y ' ' ( x ) + a 1 ( x ) y ' ( x ) + a 0 ( x ) y ( x ) = f ( x ) , y ( i ) ( T ) = c y ( i ) ( 0 ) , i = 0 , 1 , 2 ; 0 < c < 1 with a 2 , a 1 , a 0 C [ 0 , T ] for some arbitrary positive real number T , by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients a 2 , a 1 and a 0 which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon...

Periodic solutions for some nonautonomous p ( t ) -Laplacian Hamiltonian systems

Liang Zhang, X. H. Tang (2013)

Applications of Mathematics

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In this paper, we deal with the existence of periodic solutions of the p ( t ) -Laplacian Hamiltonian system d d t ( | u ˙ ( t ) | p ( t ) - 2 u ˙ ( t ) ) = F ( t , u ( t ) ) a.e. t [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 . Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.