Forced oscillations of boundary value problems of higher order functional partial differential equations
The paper deals with oscillation of solutions of higher order functional partial differential equations \[ {\partial^{2n}u \over \partial t^{2n}} +a(t) {\partial^{2n-1}u \over \partial t^{2n-1}}+ \sum^m_{i=1} p_i\biggl(x,t,u(x,t), u\bigl(x,\gamma_i(t) \bigr)\biggr) =\sum^k_{j=1} \lambda_j(t) \Delta u\bigl(x,\tau_j (t)\bigr) +f(x,t), \tag{1} \] \((x,t)\in \Omega \times [0,+\infty)\), \(\Omega \subset \mathbb{R}^n\) subject to one of the boundary conditions: \[ (2) \quad {\partial u\over \partial \nu} +\mu(x,t)u=0, \quad \text{or} \qquad (3) \quad {\partial u\over \partial\nu} =g(x,t) \text{ on } \partial \Omega\times [0,+\infty). \] The authors use the averaging technique to obtain sufficient conditions for oscillation of the solutions of problems (1), (2) and (1), (3).
higher order functional partial differential equations
scientific article; zbMATH DE number 1063996