Person:
López Gómez, Julián

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First Name
Julián
Last Name
López Gómez
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Químicas
Department
Análisis Matemático Matemática Aplicada
Area
Matemática Aplicada
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Now showing 1 - 10 of 14
  • Publication
    Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier
    (Springer Nature, 2022-12-21) López Gómez, Julián; Sampedro Pascual, Juan Carlos
    In this paper, we prove an analogue of the uniqueness theorems of Führer [15] and Amann and Weiss [1] to cover the degree of Fredholm operators of index zero constructed by Fitzpatrick, Pejsachowicz and Rabier [13], whose range of applicability is substantially wider than for the most classical degrees of Brouwer [5] and Leray–Schauder [22]. A crucial step towards the axiomatization of this degree is provided by the generalized algebraic multiplicity of Esquinas and López-Gómez [8, 9, 25], χ, and the axiomatization theorem of Mora-Corral [28, 32]. The latest result facilitates the axiomatization of the parity of Fitzpatrick and Pejsachowicz [12], σ(⋅,[a,b]), which provides the key step for establishing the uniqueness of the degree for Fredholm maps.
  • Publication
    Algebraic multiplicity and topological degree for Fredholm operators
    (Elsevier, 2020) López Gómez, Julián; Sampedro Pascual, Juan Carlos
    This paper tries to establish a link between topological and algebraic methods in nonlinear analysis showing how the topological degree for Fredholm operators of index zero of Fitzpatrick, Pejsachowicz and Rabier [11] can be determined from the generalized algebraic multiplicity of Esquinas and López-Gómez [8], [7], [22], in the same vein as the Leray–Schauder degree can be calculated from the Schauder formula through the classical algebraic multiplicity.
  • Publication
    A spatially heterogeneous predator-prey model
    (American Institute of Mathematical Sciences, 2021) López Gómez, Julián; Muñoz Hernández, Eduardo
    This paper introduces a spatially heterogeneous diffusive predator-prey model unifying the classical Lotka{Volterra and Holling{Tanner ones through a prey saturation coefficient, m(x), which is spatially heterogenous and it is allowed to ?degenerate'. Thus, in some patches of the territory the species can interact according to a Lotka{Volterra kinetics, while in others the prey saturation effects play a significant role on the dynamics of the species. As we are working under general mixed boundary conditions of non-classical type, we must invoke to some very recent technical devices to get some of the main results of this paper.
  • Publication
    The Poincaré–Birkhoff Theorem for a Class of Degenerate Planar Hamiltonian Systems
    (De Gruyter, 2021-07-17) López Gómez, Julián; Muñoz Hernández, Eduardo; Zanolin, Fabio
    In this paper, we investigate the problem of the existence and multiplicity of periodic solutions to the planar Hamiltonian system x' = −λα(t)f (y), y' = λβ(t)g(x), where α, β are non-negative T-periodic coefficients and λ > 0. We focus our study to the so-called “degenerate” situation, namely when the set Z := supp α ∩ supp β has Lebesgue measure zero. It is known that, in this case, for some choices of α and β, no nontrivial T-periodic solution exists. On the opposite, we show that, depending of some geometric configurations of α and β, the existence of a large number of T-periodic solutions (aswell as subharmonic solutions) is guaranteed (for λ > 0 and large). Our proof is based on the Poincaré–Birkhoff twist theorem. Applications are given to Volterra’s predator-prey model with seasonal effects.
  • Publication
    The structure of the set of 1-node solutions of a class of degenerate BVP's
    (Elsevier, 2020-04) López Gómez, Julián; Rabinowitz, P. H.
    A recent study, [12], [13], of a class of degenerate BVP's showed that there were two possibilities for the structure of the set of 1-node solutions. Left open was the question of whether each one was possible. Using some elementary phase plane techniques combined with some comparison arguments obtained from the maximum principle, this paper constructs examples showing that indeed each can occur.
  • Publication
    Regular versus singular solutions in quasilinear indefinite problems with sublinear potentials
    (Elsevier, 2023-06-30) López Gómez, Julián; Omari, Pierpaolo
  • Publication
    The Picone identity: a device to get optimal uniqueness results and global dynamics in Population Dynamics
    (Elsevier, 2021-01-15) Fernández Rincón, Sergio; López Gómez, Julián
    This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.
  • Publication
    Rich dynamics in planar systems with heterogeneous nonnegative weights
    (American Institute of Mathematical Sciences (AIMS), 2023-04) López Gómez, Julián; Muñoz Hernández, Eduardo; Zanolin, Fabio
    This paper studies the global structure of the set of nodal solutions of a generalized Sturm–Liouville boundary value problem associated to the quasilinear equation −(φ(u'))' = λu + a(t)g(u), λ ∈ R, where a(t) is non-negative with some positive humps separated away by intervals of degeneracy where a ≡ 0. When φ(s) = s this equation includes a generalized prototype of a classical model going back to Moore and Nehari [35], 1959. This is the first paper where the general case when λ ∈ R has been addressed when a ≥ 0. The semilinear case with a ≤ 0 has been recently treated by López-Gómez and Rabinowitz [28, 29, 30].
  • Publication
    On the applicability of the poincaré–Birkhoff twist theorem to a class of planar periodic predator-prey models
    (American Institute of Mathematical Sciences, 2020-04) López Gómez, Julián; Muñoz Hernández, Eduardo; Zanolin, Fabio
    This paper studies the existence of subharmonics of arbitrary order in a generalized class of non-autonomous predator-prey systems of Volterra type with periodic coefficients. When the model is non-degenerate it is shown that the Poincaré–Birkhoff twist theorem can be applied to get the existence of subharmonics of arbitrary order. However, in the degenerate models, whether or not the twist theorem can be applied to get subharmonics of a given order might depend on the particular nodal behavior of the several weight function-coefficients involved in the setting of the model. Finally, in order to analyze how the subharmonics might be lost as the model degenerates, the exact point-wise behavior of the T-periodic solutions of a non-degenerate model is ascertained as a perturbation parameter makes it degenerate.