We shall prove the existence of minimizers of the following functional f(u) = R T 0 L(x, u(x), u â€²(x)) dx without convexity assumption. As a consequence of this result and the duality described inâ€¦ (More)

The continuous dependence of solutions for a certain class of elliptic PDE on functional parameters is studied in this paper. The main result is as follow: the sequence {xk}kâˆˆN of solutions of theâ€¦ (More)

The paper is devoted to a system of semilinear PDEs containing gradient terms. Applying the approach based on Sattingerâ€™s iteration procedure we use sub and supersolutions methods to prove theâ€¦ (More)

where Î±, Î², Î³, Î´ â‰¥ 0, v âˆˆ V âŠ‚ {w âˆˆ L(0, 1); w : (0, 1)â†’ (âˆ’b, b)} (V 6= âˆ…), q > 1. Many problems modeled by (1.1) arise in various areas of applied mathematics, in biological, chemical or physicalâ€¦ (More)

We investigate the existence of positive solutions for the following class of nonlinear elliptic problems div(a(â€–xâ€–)âˆ‡u(x)) + f (x, u(x))âˆ’ (u(x))âˆ’Î±â€–âˆ‡u(x)â€–Î² + g(â€–xâ€–)x Â· âˆ‡u(x) = 0, where x âˆˆ Rn and â€–xâ€–â€¦ (More)