Contents -- Preface -- Photos of the homage -- A priori Bounds for the Positive Solutions of Super-Linear Indefinite Weighted Elliptic Problems -- 1. Introduction -- 2. Principal Eigenvalues and Positive Solutions -- 3. Class A(Q) of Admissible Potentials in Q -- 4. A Priori Bounds for the Positive Solutions of (1) -- Coincidence Degree and Multidimensional Resonant Problems -- 1. Introduction -- 2. Description of the problem -- 3. Qualitative study of the range -- 4. Final remarks -- Uniqueness of the Neumann Condition and Comparison Results for Dirichlet Pseudo-Monotone Problems -- 1. Introduction -- 2. Uniqueness of the Neumann condition -- 3. Two uniqueness results for pseudomonotone problems on W1p(Q) p>2 -- Parametric Excitation in a Predator-Prey Model -- 1. Introduction -- 2. Existence of a w-periodic solution. Dissipativeness -- 3. Existence of a non-trivial w -periodic solution -- 4. Hopf Bifurcation. Parametric excitation -- 5. Averaging and results -- Reasons for a Homage -- 1. First papers -- 2. Functional Analysis -- 3. Ordinary differential equations -- 4. Partial differential equations -- 5. Function theory -- 6. Textbooks -- 7. History of Mathematics -- Local Bifurcation for Elliptic Problems -- Neumann versus Dirichlet Boundary Conditions -- 1. Introduction -- 2. Local qualitative behavior -- Bifurcation through Higher Order Terms for Problems at Resonance -- 1. Introduction -- 2. The main result -- 3. Application to a boundary value problem -- Positive Solutions of a Singular Ordinary Differential Equation Relevant in Mathematical Physics -- 1. Introduction -- 2. Some auxiliary inequalities and functional setting -- 3. Some basic properties of solutions of equation (2) -- 4. Solutions in bounded intervals -- 5. Solutions in the half-line.

Large Subharmonics of Pendulum-Like Equations -- 1. Introduction -- 2. Main results -- 3. Possible generalizations -- 4. The proof of Theorem 1 -- Four Theorems and One Conjecture on the Global Asymptotic Stability of Delay Differential Equations -- 1. Introduction -- 2. First theorem -- 3. Second theorem -- 4. Third theorem -- 5. Fourth theorem -- 6. The conjecture -- Malthus Verhulst and the Metasolutions -- 1. Introduction -- 2. Malthus's law -- 3. Verhulst's law -- 4. General case: the theory of metasolutions -- The Legacy of Pierre-Frangois Verhulst and Vito Volterra in Population Dynamics -- 1. Verhulst's first two papers on the law of population -- 2. Verhulst's third paper on the law of population -- 3. Verhulst's purgatory and resurrection -- 4. Single population in a changing environment -- 5. Volterra's model for the struggle for life -- 6. Experiments and models for other interactions -- 7. Several species in a varying environment -- 8. Conclusion -- Numerical Simulation of Local Cooperation Strategies in Competitive Environments -- 1. Introduction -- 2. Numerical study -- Axiomatizing the Algebraic Multiplicity -- 1. Introduction -- 2. The multiplicity of R. J. Magnus -- 3. The uniqueness theorems -- 4. Applications. Multiplicity formulae -- Instability of Periodic Solutions Obtained by Minimization -- 1. Introduction -- 2. The Levi-Civita reduction -- 3. The index of degenerate minimizers -- Some Recent Results on Semilinear Sturm-Liouville Problems with Jumping Nonlinearities -- 1. Introduction -- 2. Notation -- 3. Half-eigenvalues -- 4. Multiplicity results -- 5. Solvability properties -- 6. The Fucik spectrum -- Periodic Solutions of Second Order Equations - A Variational Approach -- 1. Introduction -- 2. The problem -- 3. Sobolev spaces functionals variational inequalities.

4. Sub- and supersolutions -- 5. Extensions to elliptic PDE -- Some Indefinite Nonlinear Eigenvalue Problems -- 1. Introduction -- 2. Proof of Theorem 1 -- 3. The particular case K = 1 -- Coincidence Degree and Coexistence States for Periodic Kolmogorov Systems -- 1. Introduction notation and basic setting -- 2. Coexistence states for Kolmogorov systems -- 3. The shooting method versus the functional analytic approach: an application to planar competitive systems -- 4. Computation of the Brouwer degree for a vector field in R3 possessing a cyclic symmetry.