Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient

In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set. Our approach is based on Leray-Schauder alternative principle, method of sub-supersolution, nonlinear regularity, truncation techniques, and set-valued analysis

Convergence of optimal solutions in control problems for hyperbolic equations

A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the parameter k. We deal with the limit behaviour, as k → ∞, of the sequence of optimal solutions using the notions of G- and Γ-convergences. The conditions under which this sequence converges to an optimal solution for the limit problem are given

Existence and relaxation results for nonlinear evolution inclusions revisited

In this paper we confirm the validity of some recent results of Hu, Lakshmikantham, Papageorgiou [4] and Papageorgiou [13] concerning the existence and relaxation for nonlinear evolution inclusions. We fill a gap in the proofs of these results due to the use of incorrect Nagy's compactness embedding theorem

Sensitivity of the Solution Set to Second Order Evolution Inclusions

International audienceIn this note we study second order evolution inclusions in the framework of evolution triple of spaces. The existence of mild solutions (i.e. trajectory-selection pairs) to the inclusion, and the upper and lower semicontinuity properties of the solution set with respect to a parameter are established

Evolutionary inclusions and hemivariational inequalities

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