We give a simple explicit description of the norm in the complex interpolation space (Cp[Lp(M)], Rp[Lp(M)])θ for any von Neumann algebra M and any 1 ≤ p ≤ ∞.

Maz'ja and Sinnamon proved a characterization of the boundedness of the Hardy operator from Lp(v) into Lq(w) in the case 0 < q < p, 1 < p < ∞. We present here a new simple proof of the sufficiency part of that result.

We consider the stability of periodic travelling-wave solutions to a generalized Korteweg–de Vries (gKdV) equation and prove an index theorem relating the number of unstable and potentially unstable eigenvalues to geometric ...

We use the extended multiple Riccati equations expansion method to construct a series of double-soliton-like solutions, double triangular function solutions and complexiton soliton solutions for nonlinear Jaulent-Miodek ...

We consider an inverse parabolic problem of reconstruction of the source function, together with the traditional solution. In contrast with older literature, we consider non-homogeneous and time-dependent boundary conditions. ...

The Hermite-Hadamard inequality not only is a consequence of convexity but also characterizes it: if a continuous function satisfies either its left-hand side or its right-hand side on each compact subinterval of the domain, ...

For a sign-changing function a(x) we consider the solutions of the following semilinear elliptic problem in ℝn with n ≥ 3: $$-\Delta{u}=(\gamma a^{+}-a^{-})u^{q}+u^{p},\qq u\ge0\link{and} u\in\mathcal{D}(\mathbb{R}^{n}),$$ ...

This note extends the results in ‘Optimal coercivity inequalities in W1,p(Ω)’ (G. Auchmuty, Proc. R. Soc. Edinb. A 135, 915–933.) describing the dependence of the optimal constant in the p-version of Friedrichs' inequality ...

This paper is concerned with the dynamics of a non-local delayed reaction–diffusion equation without quasi-monotonicity on an infinite n-dimensional domain, which can be derived from the growth of a stage-structured ...

By using the symmetric mountain pass theorem, we establish some new existence criteria to guarantee that the second-order Hamiltonian systems ü(t) − L(t)u(t) + ∇W(t,u(t)) = 0 have infinitely many homoclinic orbits, where ...