Download Analysis and Topology in Nonlinear Differential Equations: A by Djairo G de Figueiredo, João Marcos do Ó, Carlos Tomei PDF

By Djairo G de Figueiredo, João Marcos do Ó, Carlos Tomei

This quantity is a suite of articles offered on the Workshop for Nonlinear research held in João Pessoa, Brazil, in September 2012. The effect of Bernhard Ruf, to whom this quantity is devoted at the party of his sixtieth birthday, is perceptible during the assortment through the alternative of issues and methods. the various individuals examine smooth themes within the calculus of adaptations, topological tools and regularity research, including novel purposes of partial differential equations. in response to the culture of the workshop, emphasis is given to elliptic operators inserted in several contexts, either theoretical and utilized. issues comprise semi-linear and entirely nonlinear equations and structures with diverse nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi sort. additionally handled are analytic points in addition to purposes similar to diffusion difficulties in mathematical genetics and finance and evolution equations regarding electromechanical devices.

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Extra resources for Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday

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Mathematics Subject Classification (2010). 35J20; 35J60; 46E35. Keywords. Nonlinear elliptic equations, zero mass case, unbounded cylinders, variational and perturbative methods, compact imbeddings. 1. R. (research funds PRIN 2009 and ex 60%). 40 S. Barile and A. Salvatore N − m ≥ 2, m ≥ 1, Ω ⊂ Rm open smooth bounded. We restrict to the case where g(x, u) behaves as a superlinear but subcritical power up−1 at infinity with 2 < p < 2∗ , where 2∗ = N2N −2 . , Rabinowitz [27] and references within) have looked for solutions of elliptic equations with zero Dirichlet boundary conditions by variational methods.

6. 3. Multiplicity Results 43 The paper is organized as follows: in Section 2, we introduce the variational formulation of the problems and suitable “partially” spherically symmetric Sobolev spaces. We overcome the lack of compactness of the problems by recalling some compact Sobolev imbeddings for such spaces. 1. In Section 4, we recall Bolle’s perturbation method and multiplicity results for perturbed problems. 4. 4. , 1t + t1 = 1; • ai , ci , Ci denote suitable positive constants. 2. Variational framework In order to prove that problem (Pf ) and consequently (P0 ) has a variational structure, let us consider the space W01,2 (Ω) endowed with the norm ||u|| = |∇u| dx 2 1 2 .

Mathematics Subject Classification (2010). 35J20; 35J60; 46E35. Keywords. Nonlinear elliptic equations, zero mass case, unbounded cylinders, variational and perturbative methods, compact imbeddings. 1. R. (research funds PRIN 2009 and ex 60%). 40 S. Barile and A. Salvatore N − m ≥ 2, m ≥ 1, Ω ⊂ Rm open smooth bounded. We restrict to the case where g(x, u) behaves as a superlinear but subcritical power up−1 at infinity with 2 < p < 2∗ , where 2∗ = N2N −2 . , Rabinowitz [27] and references within) have looked for solutions of elliptic equations with zero Dirichlet boundary conditions by variational methods.

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