Rodrigues-type formulae for Hermite and Laguerre polynomials.
Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media.
Existence and nonexistence of entire solutions to the logistic differential equation.
A saddle point theorem for non-smooth functionals and problems at resonance.
Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations
Let (M,g) be a compact Riemannian manifold without boundary, with dim M ≥ 3, and f: ℝ → ℝ a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem , σ ∈ M, ω ∈ H₁²(M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, stands for the Laplace-Beltrami operator on (M,g), and α, K̃ are smooth positive functions. These multiplicity...
Explosive solutions of semilinear elliptic systems with gradient term.
Estudiamos la existencia de soluciones del sistema elíptico no lineal Δu + |∇u| = p(|x|)f(v), Δv + |∇v| = q(|x|)g(u) en Ω que explotan en el borde. Aquí Ω es un dominio acotado de R o el espacio total. Las nolinealidades f y g son funciones continuas positivas mientras que los potenciales p y q son funciones continuas que satisfacen apropiadas condiciones de crecimiento en el infinito. Demostramos que las soluciones explosivas en el borde dejan de existir si f y g son sublineales. Esto se tiene...
The Impact of the Mountain Pass Theory in Nonlinear Analysis: a Mathematical Survey
We provide a survey on the mountain pass theory, viewed as a central tool in the modern nonlinear analysis. The abstract results are illustrated with relevant applications to nonlinear partial differential equations.
Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
On the Ginzburg-Landau energy with weight
Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket
Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.
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