Semilinear problems with bounded nonlinear term

Semilinear Problems with Bounded Nonlinear Term

Resonant semilinear problems with nonlinear term depending on the derivative ✩

We study the existence of solution for a boundary value problem at resonance where the nonlinearity depends only on the derivative. In a sense, we can say that the problem considered is strongly resonant. Our proofs make use of the Lyapunov–Schmidt reduction; in so doing, we are led with the asymptotic estimate of the corresponding bifurcation equation.  2004 Elsevier Inc. All rights reserved.

Semilinear Elliptic Boundary-value Problems on Bounded Multiconnected Domains

A semilinear elliptic boundary-value problem on bounded multiconnected domains is studied. The authors prove that under suitable conditions, the problem may have no solutions in certain cases and many have one or two nonnegative solutions in some other cases. The radial solutions were also studied in annular domains.

Existence of Positive Bounded Solutions of Semilinear Elliptic Problems

Correspondence should be addressed to Faten Toumi, [email protected] Received 18 June 2010; Accepted 25 September 2010 Academic Editor: A. Mikelic Copyright q 2010 Faten Toumi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Thi...

Semilinear parabolic problems