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In this work we study existence and multiplicity questions for positive solutions of second-order semilinear elliptic boundary value problems, where the nonlinearity is multiplied by a weight function which is allowed to change sign and vanish on sets of positive measure. We do not impose a variational structure, thus techniques from the calculus of variations are not applicable. Under various qualitative assumptions on the nonlinearity we establish a priori bounds and employ bifurcation and fixed point index theory to prove existence and multiplicity results for positive solutions. In an appendix we derive interior L p -estimates for general elliptic systems of arbitrary order under minimal smoothness hypotheses. Special instances of these results are used in the derivation of a priori bounds. Academic Press

In this work we deal with the problem of the existence and uniqueness of principal eigenvalues for some linear weighted boundary value problems associated to a general second order uniformly elliptic operator. For a large class of sign definited weights, we characterize whether the boundary value problem admits a principal eigenvalue or not.

We derive a result on the limit of certain sequences of principal eigenvalues associated with some elliptic eigenvalue problems. This result is then used to give a complete description of the global structure of the curves of positive steady states of a parameter dependent diffusive version of the classical logistic equation. In particular, we characterize the bifurcation values from infinity to positive steady states. The stability of the positive steady states as well as the asymptotic behaviour of positive solutions is also discussed.

The Iberian Basin was an intracratonic rift basin in central-eastern Spain developed since Early Permian times. The basin boundary faults were normal, listric faults controlling an asymmetric extension propagating northeast with time.Hercynian or older lineaments controlled the orientation of the Iberian Basin and extension was accommodated basically in the hanging wall block by the formation of secondary grabens and a central high. The basin was related with the coeval Ebro, Catalan and Cuenca-Mancha Basins and their connections are discussed.Subsidence curves show that the Early Permian-Early Jurassic period of extension can be subdivided into three rifting episodes and a flexural one. Extension factor increases from 1.17 in the northwest to 1.29 near the Mediterranean coast.The increasing extension rate was accommodated by transfer faults trending NNE-SSW, more important in the Levante area. The rift evolution is intermittent and seems to reflect distinct stress fields.The collapse of the late Hercynian orogen and related increased heat flux, extension and rifting is the most probable origin of the Iberian Basin and related basins. The origin of the Catalan and the Valencia-Prebetic Basins is related to the southwards migration of the Hesse-Burgundy Rift along the eastern margin of the Iberian Microplate.

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In this paper we analyze how the dynamics of a class of superlinear indefinite reaction diffusion equations varies as the nodal behavior of a coefficient changes.To perform this analysis we use both theoretical and numerical tools. The analysis aids the numerical study, and the numerical study confirms and completes the analysis. The numerics in addition provides us with some further results for whichat-first glance analytical tools are not available yet. Our main analytical result shows that the problem possesses a unique positive solution which is linearly asymptotically stable if the trivial state is linearly unstable and the model admits some positive solution. This result is a relevant feature for superlinear indefinite problems, since our numerical computations show how these models can have an arbitrarily large number of positive solutions if the trivial state is unstable. 2000Academic Press

In this work we analyze the existence, stability, and multiplicity of coexistence states for a symbiotic Lotka Volterra model with general diffusivities and transport effects. Global bifurcation theory, blowing up arguments for a priori bounds, singular perturbation results, singularity theory, and fixed point index in cones are among the techniques used to get our results and to explain the drastic change of behavior exhibited by the dynamics of the model between the cases of weak and strong mutualism between the species. Our methodology works out to treat much more general classes of symbiotic models. Academic PressKey Words: blowing up for a priori bounds in systems; local and global bifurcation theory; singularity theory; fixed point index in cones; singular perturbations.