Positive solutions for a nonlocal boundary-value problem with vector-valued response.
Sufficient optimality conditions for multivariable control problems
We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.
Shape optimization of control problems described by wave equations
Nonhomogeneous boundary value problem for a semilinear hyperbolic equation
We discuss the solvability of a nonhomogeneous boundary value problem for the semilinear equation of the vibrating string in a bounded domain and with a certain type of superlinear nonlinearity. To this end we derive a new dual variational method.
Dual dynamic approach to shape optimization
On the existence of multiple solutions for a nonlocal BVP with vector-valued response
The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.
Existence of solutions for the Dirichlet problem with superlinear nonlinearities
In this paper we establish the existence of nontrivial solutions to with superlinear in .
Correction to the paper “Existence of solutions for the Dirichlet problem with superlinear nonlinearities”
Page 1