By Djairo G de Figueiredo, João Marcos do Ó, Carlos Tomei
This quantity is a suite of articles provided on the Workshop for Nonlinear research held in João Pessoa, Brazil, in September 2012. The impact of Bernhard Ruf, to whom this quantity is devoted at the celebration of his sixtieth birthday, is perceptible during the assortment by way of the alternative of subject matters and methods. the various individuals ponder glossy themes within the calculus of adaptations, topological tools and regularity research, including novel functions of partial differential equations. in line with the culture of the workshop, emphasis is given to elliptic operators inserted in numerous contexts, either theoretical and utilized. subject matters comprise semi-linear and entirely nonlinear equations and structures with diverse nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi style. additionally handled are analytic elements in addition to functions resembling diffusion difficulties in mathematical genetics and finance and evolution equations regarding electromechanical devices.
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Extra info for Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday
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Since EG = W01,2 (Ω) ∩ Fix(G) → WG1,2 (Ω), it follows that EG → → Lt (Ω) for 2 < t < 2∗ . 1. 3. 1, it follows that dϕ1 is compact from EG in EG . 46 S. Barile and A. Salvatore Proof. , E → L t0 −1 (Ω). , 2 2∗ < t0 < , p−1 p−1 ⎪ 2∗ ⎪ ⎩ < t0 < 2, 2∗ − 1 is solvable because, as 2 < p < 2∗ , max 2 2∗ , ∗ p−1 2 −1 < min 2∗ , 2 . 20]). 4. 7) does not hold for t = 2. 3. 9]) to the functional J0 . In order to do this, we ﬁrst recall the following Palais–Smale condition, brieﬂy (PS). 1. 2) converges in EG , up to subsequences.