We study the existence of homoclinic solutions for semilinear p−Laplacian difference equations with periodic coefficients. The proof of the main result is based on Brezis–Nirenberg’s Mountain Pass Theorem. Several examples and remarks are given.

The paper is concerned with conservative solutions to the nonlinear wave equation utt−c(u) ( c(u)ux ) x = 0. For an open dense set of C initial data, we prove that the solution is piecewise smooth in the t-x plane, while the gradient ux can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a sem...

Abstract. We discuss a general framework for the numerical solution of a family of semilinear elliptic problems whose leading differential operator is the Laplacian. A problem is first transformed to one on a standard domain via a conformal mapping. The boundary value problem on the standard domain is then reduced to an equivalent integral operator equation. We employ the Galerkin method to sol...

This paper is devoted to establishing local and global existence theorems for autonomous semilinear parabolic initial value problems. The local existence theorems do not require Lipchitz condition on nonlinear term. The global existence theorem is an extension of the well-known result of Fujita-Weissler for semilinear heat equations to general autonomous semilinear parabolic equations and systems.

A semilinear space S is homogeneous if, whenever the semilinear structures induced on two finite subsets S1 and S2 of S are isomorphic, there is at least one automorphism of S mapping S1 onto S2. We give a complete classification of all finite homogeneous semilinear spaces. Our theorem extends a result of Ronse on graphs and a result of Devillers and Doyen

A construction of finite semifield planes of order n using irreducible semilinear transformations on a finite vector space of size n is shown to produce fewer than √ n log2 n different nondesarguesian planes.

have been extensively studied. Various existence and uniqueness results are given in [1], [2], and [3], to name a few. More recently, in [4], it is shown that by certain transformations the boundary layer equations for the class of non-Newtonian uids named pseudoplastic can be generalized in the above form for the ODE case n = 1. Under this physical interpretation the above equation, considered...

when p = , |f (x,u)| ≤ c(|u|+ |u|q–),  < q≤ ∗ = N N– ,N ≥ , for the corresponding results onemay refer to Brézis [], Brézis and Nirenberg [], Bartsch andWillem [] and Capozzi, Fortunato and Palmieri []. Garcia and Alonso [] generalized Brézis, Nirenberg’s existence and nonexistence results to p-Laplace equation. Moreover, let us consider the following semilinear Schrödinger equation:

Under simple conditions on fi and gi, we show the existence of entire positive radial solutions for the semilinear elliptic system ∆u = p(|x|)f1(v)f2(u) ∆v = q(|x|)g1(v)g2(u), where x ∈ RN , N ≥ 3, and p, q are continuous functions.

In this paper we give a necessary and sufficient conditions for approximate controllability of a wide class of semilinear nonautonomous systems in Hilbert spaces. This is done by employing skew-product semi-flows technique. As an application we prove the approximate controllability of a broad class of nonautonomous semilinear reaction diffusion equations which includes the semilinear heat equat...