Books by Julian Lopez-Gomez

Analyze Global Nonlinear Problems Using MetasolutionsMetasolutions of Parabolic Equations in Population Dynamics explores the dynamics of a generalized prototype of semilinear parabolic logistic problem. Highlighting the authorΓÇÖs advanced work in the field, it covers the latest developments in the theory of nonlinear parabolic problems.The book reveals how to mathematically determine if a species maintains, dwindles, or increases under certain circumstances. It explains how to predict the time evolution of species inhabiting regions governed by either logistic growth or exponential growth. The book studies the possibility that the species grows according to the Malthus law while it simultaneously inherits a limited growth in other regions.The first part of the book introduces large solutions and metasolutions in the context of population dynamics. In a self-contained way, the second part analyzes a series of very sharp optimal uniqueness results found by the author and his colleagues. The last part reinforces the evidence that metasolutions are also categorical imperatives to describe the dynamics of huge classes of spatially heterogeneous semilinear parabolic problems. Each chapter presents the mathematical formulation of the problem, the most important mathematical results available, and proofs of theorems where relevant.

Addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators.

This book explores the dynamics of a generalized prototype of semilinear parabolic logistic problem. The first part of the book introduces large solutions and metasolutions in the context of population dynamics. In a self-contained way, the second part analyzes a series of very sharp optimal uniqueness results found by the author and his colleagues. The last part reinforces the evidence that metasolutions are also categorical imperatives to describe the dynamics of huge classes of spatially heterogeneous semilinear parabolic problems.

Addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators.