Three nontrivial solutions for the p-Laplacian Neumann problems with a concave nonlinearity near the origin

We consider a nonlinear Neumann problem driven by the p- Laplacian, with a right-hand side nonlinearity which is concave near the origin. Using variational techniques, combined with the method of upper-lower solutions and with Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have a constant sign (one positive and one negative).FCTPOCI/MAT/55524/200

Resonant nonlinear periodic problems with the scalar p-Laplacian and a nonsmooth potential

We study periodic problems driven by the scalar p-Laplacian with a nonsmooth potential. Using the nonsmooth critical point theory for locally Lipsctiz functions,we prove two existence theorems under conditions of resonance at infinity with respect to the first two eigenvalues of the negative scalar p-Laplacian with periodic boundary conditions.Universidade de Aveir

On the long-time behaviour of compressible fluid flows subjected to highly oscillating external forces

summary:We show that the global-in-time solutions to the compressible Navier-Stokes equations driven by highly oscillating external forces stabilize to globally defined (on the whole real line) solutions of the same system with the driving force given by the integral mean of oscillations. Several stability results will be obtained

On a nonlinear integrodifferential equation

Digitalitzat per Nubilu

Infinitely many nodal solutions for anisotropic (p, q)-equations

We consider an anisotropic (p.q)-Neumann problem with an indefinite potential term and a reaction which is only locally defined and odd. Using a variant of the symmetric mountain pass theorem, we show that the problem has a whole sequence of smooth nodal solutions which converge to zero in C1Ω.publishe

Nonlinear nonhomogeneous logistic equations of superdiffusive type

We consider a nonlinear logistic equation of superdiffusive type driven by a nonhomogeneous differential operator and a Robin boundary condition. We prove a multiplicity result for positive solutions which is global with respect to the parameter λ > 0 (bifurcation-type theorem). We also demonstrate the existence of a minimal positive solution uλ and determine the monotonicity and continuity properties of the minimal solution map λ → uλ.publishe

Semilinear neumann equations with indefinite and unbounded potential

We consider a semilinear Neumann problem with an indefinite and unbounded potential, and a Carathéodory reaction term. Under asymptotic conditions on the reaction which make the energy functional coercive, we prove multiplicity theorems producing three or four solutions with sign information on them. Our approach combines variational methods based on the critical point theory with suitable perturbation and truncation techniques, and with Morse theory

Multiple solutions with sign information for (p, 2)−equations with asymmetric resonant reaction

We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p−Laplacian and a Laplacian (a (p, 2)− equation). The reaction is the sum of two competing terms, a parametric (p − 1)−sublinear term and an asymmetric (p − 1)−linear perturbation which is resonant at −∞. Using variational methods together with truncations and comparison techniques and Morse theory (critical groups), we prove two multiplicity theorems which provide sign information for all the solutions.publishe