This monograph is devoted to the study of nonconvex optimal control and variational
problems. It contains a number of recent results obtained by the author in the last 15 years …

The Tonelli existence theorem in the calculus of variations and its subsequent modifications
were established for integrands f which satisfy convexity and growth conditions. In AJ …

Existence of solutions of optimal control problems for a generic integrand without convexity
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This paper concerns with the existence of solutions in optimal control problems governed by
systems of ordinary differential equations. It is well known that existence questions for …

We are concerned with the problem of existence, uniqueness and qualitative properties of
solutions to the radially symmetric variational problem u∈\Wuu(B_R)B_Rfx,∇u(x)+h(|x|,u(x)) …

We first prove a new Lyapunov-type theorem which will yield existence of solutions to
nonconvex minimum problems involving some hyperbolic equations on rectangular …

In this paper we suggest a direct method for studying local minimizers of one-dimensional
variational problems which naturally complements the classical local theory. This method …

Consider the minimization problem (P) min\left {\int_0^ 1 f\left (t, u'\left (t\right)\right) dt; u ∈
W^ 1.1\left (\left 0, 1\right, R''\right), u\left (0\right)= u_0, u\left (1\right)= u_1\right\}, in which …

The purpose of this paper is to establish an existence result for nonconvex variational
problems with Bochner integral constraints in separable Asplund spaces via the Euler …

We are concerned with the problem of existence of solutions to the variational problem
\min\left{\int_0^Rg(t,v'(t))\,dt;\v∈AC(0,R),\v(R)=0\right\}, with only one fixed endpoint …