Nonlinear second-order multivalued boundary value problems

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the `convex' and `nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.Comment: 26 page

Multiplicity of positive solutions for a degenerate nonlocal problem with p-Laplacian

We consider a nonlinear boundary value problem with degenerate nonlocal term depending on the Lq-norm of the solution and the p-Laplace operator. We prove the multiplicity of positive solutions for the problem, where the number of solutions doubles the number of "positive bumps"of the degenerate term. The solutions are also ordered according to their Lq-norms

Realistic expectations for the treatment of FMGP residuals by chemical oxidants

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.jconhyd.2018.08.007 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/Methods to remediate soil and groundwater contamination at former manufactured gas plant (FMGP) sites are scarce. The objective of this study was to investigate the ability of two chemical oxidants (persulfate and permanganate) to degrade FMGP residuals in a dynamic system representative of in situ conditions. A series of physical model trials supported by aqueous and slurry batch experiments using impacted sediments collected from a FMGP site were conducted. To explore treatment expectations a screening model constrained by the experimental data was employed. The results from the aqueous experiments showed that dissolved components (except for benzene) were readily degraded by persulfate or permanganate. In the well-mixed slurry systems, when contact with the oxidant was achieved, 95%, 45% and 30% of the initial mass quantified was degraded by permanganate, unactivated persulfate, and alkaline activated persulfate, respectively. In stark contrast, the total mass removed in the physical model trials was negligible for both permanganate and persulfate irrespective of the bleb or lense architecture used. Hence the net benefit of flushing 6 pore volumes of permanganate or persulfate at a concentration of 30 g/L under the physical model operating conditions was minimal. To achieve a substantial degradation of mass within the treatment system (>40%), results from the screening model indicated that the hydraulic resident time would need to be >10 days and the average lumped mass transfer coefficient increased by two orders-of-magnitude. Results from long-term (5 years) simulations showed that the dissolved concentrations of organic compounds are reduced temporarily as a result of the presence of permanganate but then rebound to a profile that is essentially coincident with a no-treatment scenario following exposure to permanganate. Neither a lower velocity nor higher permanganate dosing affected the long-term behavior of the dissolved phase concentrations; however, increasing the mass transfer rate coefficient had an impact. The findings from this investigation indicate that the efficiency of permanganate or persulfate to treat for FMGP residuals is mass transfer limited.TECO Peoples Gas, Tampa FLNatural Sciences and Engineering Research Council (NSERC) of Canada Collaborative Research and Development Gran

Constant sign and nodal solutions for a class of nonlinear Dirichlet problems

We consider a nonlinear Dirichlet problem with a Carathéodory reaction which has arbitrary growth from below. We show that the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal. In the semilinear case (i.e., p =2), with the reaction f(z, .)being C1and with subcritical growth, we show that there is a second nodal solution, for a total of four nontrivial smooth solutions. Finally,when the reaction has concave terms and is subcritical and for the nonlinear problem (i.e., 1 <p <∞) we show that again we can have the existence of three nontrivial smooth solutions, two of constant sign and a third nodal

Parametric nonlinear resonant Robin problems

We consider a nonlinear Robin problem driven by the ▫$p$▫-Laplacian. In the reaction we have the competing effects of two nonlinearities. One term is parametric, strictly ▫$(p-1)$▫-sublinear and the other one is ▫$(p-1)$▫-linear and resonant at any nonprincipal variational eigenvalue. Using variational tools from the critical theory (critical groups), we show that for all big values of the parameter ▫$lambda$▫ the problem has at least five nontrivial smooth solutions