Displaying similar documents to “Nonlinear variational evolution inequalities in Hilbert spaces.”

Periodic problems and problems with discontinuities for nonlinear parabolic equations

Tiziana Cardinali, Nikolaos S. Papageorgiou (2000)

Czechoslovak Mathematical Journal

Similarity:

In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and...

Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space L 1 ( 0 , + ∞ ) ∩ L ∞ ( 0 , + ∞ )

Aghavard Kh. Khachatryan, Khachatur A. Khachatryan (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

The paper studies a construction of nontrivial solution for a class of Hammerstein–Nemytskii type nonlinear integral equations on half-line with noncompact Hammerstein integral operator, which belongs to space L 1 ( 0 , + ∞ ) ∩ L ∞ ( 0 , + ∞ ) . This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results. For one type of considering equations continuity and uniqueness of the solution is established.