We study minimizers of the energy functional

multiplicity of positive solutions for a class of semilinear problem. II. Junping Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability. multiplicity of positive solutions for a class of semilinear problems. Existence and instability of spike layer solutions to singular perturbation problems. J.

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281–354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold–Falk–Winther framework by analyzing variational crimes (a la...

We study the semilinear nonlocal equation ut = J∗u− u− u in the whole R . First, we prove the global well-posedness for initial conditions u(x, 0) = u0(x) ∈ L(R ) ∩ L∞(RN ). Next, we obtain the long time behavior of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J : finite time extinction for p < 1, faster than exponential decay for the ...

We deal with the unique solvability of multidimensional backward stochastic differential equations (BSDEs) with a p-integrable terminal condition (p > 1) and a superlinear growth generator. We introduce a new local condition, on the generator (see Assumption (H4)), then we show that it ensures the existence and uniqueness, as well as the L-stability of solutions. Since the generator is of super...

We study the local solvability problem for a class of semilinear equations whose linear part is the Kohn Laplacian, acting on top degree forms. We also study the validity of the Poincaré lemma, in top degree, for semilinear perturbations of the tangential Cauchy-Riemann complex.

The existence, uniqueness, regularity and asymptotic behavior of global solutions of semilinear heat equations in Hilbert spaces are studied by developing new results in the theory of one-parameter strongly continuous semigroups of bounded linear operators. Applications to special semilinear heat equations in L(R) governed by pseudo-differential operators are given.

This paper is concerned with the study of weighted pseudo almost periodic mild solutions for semilinear boundary differential equations. Namely, some sufficient conditions for the existence and uniqueness of weighted pseudo almost periodic mild solutions of semilinear boundary differential equations are obtain.