Person: Pardo San Gil, Rosa María
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First Name
Rosa María
Last Name
Pardo San Gil
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Químicas
Department
Análisis Matemático Matemática Aplicada
Area
Matemática Aplicada
Identifiers
5 results
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Now showing 1 - 5 of 5
Item Infinite resonant solutions and turning points in a problem with unbounded bifurcation(International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2010) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, AníbalSummary: "We consider an elliptic equation −Δu+u=0 with nonlinear boundary conditions ∂u/∂n=λu+g(λ,x,u) , where (g(λ,x,s))/s→0 as |s|→∞ . In [Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 2, 225--252; MR2360769 (2009d:35194); J. Differential Equations 246 (2009), no. 5, 2055--2080; MR2494699 (2010c:35016)] the authors proved the existence of unbounded branches of solutions near a Steklov eigenvalue of odd multiplicity and, among other things, provided tools to decide whether the branch is subcritical or supercritical. In this work, we give conditions on the nonlinearity, guaranteeing the existence of a bifurcating branch which is neither subcritical nor supercritical, having an infinite number of turning points and an infinite number of resonant solutions.''Item Positive solutions for slightly subcritical elliptic problems via Orlicz Spaces(Milan Journal of Mathematics, 2022) Pardo San Gil, Rosa María; Cuesta, MabelThis paper concerns semilinear elliptic equations involving sign-changing weight function and a nonlinearity of subcritical nature understood in a generalized sense. Using an Orlicz–Sobolev space setting, we consider superlinear nonlinearities which do not have a polynomial growth, and state sufficient conditions guaranteeing the Palais–Smale condition. We study the existence of a bifurcated branch of classical positive solutions, containing a turning point, and providing multiplicity of solutions.Item Equivalence between uniform Lp∗ a priori bounds and uniform L∞ a priori bounds for subcritical p-laplacian equations(Mediterranean Journal of Mathematics, 2021) Mavinga, Nsoki; Pardo, Rosa; Pardo San Gil, Rosa MaríaWe establish sufficient conditions for a uniform Lp⋆ (Ω) bound to imply a uniform L∞(Ω) bound for positive weak solutions of sub- critical p-Laplacian equations. We also provide an equivalent result for sequences of boundary-value problems. As consequences, we prove that any set of solutions with finite energy is L∞(Ω) a priori bounded, and also obtain an alternative proof of the existence of a priori bounds for subcritical power like nonlinearities.Item L∞(Ω) a priori estimates for subcritical semilinear elliptic equations with a Carathéodory non-linearity(Journal of Fixed Point Theory and Application, 2023) Pardo San Gil, Rosa MaríaWe consider a semilinear boundary value problem −Δu =f(x,u), in Ω, with Dirichlet boundary conditions, where Ω ⊂ RN with N > 2, is a bounded smooth domain, and f is a Carathéodory function, superlinear and subcritical at infinity. We provide L∞(Ω) a priori estimates for weak solutions in terms of their L2∗ (Ω)-norm, where 2*= 2N/N-2 is the critical Sobolev exponent. To establish our results, we do not assume any restrictions on the sign of the solutions, or on the non-linearity. Our approach is based on Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg interpolation inequalities. Finally, we state sufficient conditions for having H01(Ω) uniform a priori bounds for non-negative solutions, so finally we provide suficient conditions for having L∞(Ω) uniform a priori bounds, which holds roughly speaking for superlinear and subcritical non-linearities.Item Equilibria and global dynamics of a problem with bifurcation from infinity(Journal of Differential Equations, 2009) Arrieta Algarra, José María; Pardo San Gil, Rosa María; Rodríguez Bernal, AníbalWe consider a parabolic equation ut−Δu+u=0 with nonlinear boundary conditions , where as |s|→∞. In [J.M. Arrieta, R. Pardo, A. Rodríguez-Bernal, Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity, Proc. Roy. Soc. Edinburgh Sect. A 137 (2) (2007) 225–252] the authors proved the existence of unbounded branches of equilibria for λ close to a Steklov eigenvalue of odd multiplicity. In this work, we characterize the stability of such equilibria and analyze several features of the bifurcating branches. We also investigate several question related to the global dynamical properties of the system for different values of the parameter, including the behavior of the attractor of the system when the parameter crosses the first Steklov eigenvalue and the existence of extremal equilibria. We include Appendix A where we prove a uniform antimaximum principle and several results related to the spectral behavior when the potential at the boundary is perturbed.