Hyperbolic Variational Inequality of the Third Order with Variable Exponent of Nonlinearity

Cauchy problem for hyperbolic equations of third order with variable exponent of nonlinearity

“…In case A = B = −△, type (4) equations are considered in [22,26,37]. In particular, the behaviour as t → +∞ of the global solutions to the initial-boundary problems for hyperbolic equations of the third order are obtained in [37].…”

“…In particular, the behaviour as t → +∞ of the global solutions to the initial-boundary problems for hyperbolic equations of the third order are obtained in [37]. The corresponding hyperbolic variational inequalities in bounded and unbounded domain with the spatial variables are studied in [22] and [26] respectively if p(x) > 1 and q(x) ≡ 2. The existence and uniqueness theorems are proved.…”