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In this article, we study the regularizing effects of the lower order term in the case of a nonlinear elliptic problem with degenerate coercivity. We show that the presence of certain lower order terms has a regularizing effect on the solutions. The obtained results extend some existing ones. [ABSTRACT FROM AUTHOR]

We consider an abstract optimal control problem with additional constraints and nonsmooth terms, but without the requirement that both the state equation on the set of admissible controls and the extremum problem be solvable. We use the approximate penalty method proposed here to find an approximate (in the weak sense) solution of the problem. As an example, we consider the optimal control problem for a singular nonlinear elliptic type equation. [ABSTRACT FROM AUTHOR]

We establish the existence of a weak solution to the Dirichlet problem belonging to a Sobolev space for nonlinear elliptic equations of second order with right-hand sides from a wide class of functions defined in terms of the logarithmic function. [ABSTRACT FROM AUTHOR]

We study the optimal control problem for systems described by nonlinear elliptic equations. We have no information about the existence and uniqueness of the solution for some particular control. The extremum problem may be unsolvable. We regularize the problem by using a combination of the penalty method and the Tikhonov method. For the regularized problem, we prove the existence of the solution and find necessary conditions for optimality in the form of variational inequalities. We show that the regularization method used in this paper allows one to find an approximate (in some sense) solution of the original problem. [ABSTRACT FROM AUTHOR]