Download PDF by Thierry Cazenave, David Costa, Orlando Lopes, Raúl: Contributions to Nonlinear Analysis: A Tribute to D.G. de

By Thierry Cazenave, David Costa, Orlando Lopes, Raúl Manásevich, Paul Rabinowitz, Bernhard Ruf, Carlos Tomei

ISBN-10: 3764371498

ISBN-13: 9783764371494

ISBN-10: 3764374012

ISBN-13: 9783764374013

This quantity comprises learn and survey articles within the fields of nonlinear research and nonlinear differential equations, written via across the world complete researchers. The articles mirror the cutting-edge in those very important fields of present learn. the quantity is devoted to D.G. de Figueiredo, thereby honoring the $64000 contributions and lasting impression of a exceptional mathematician.

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By Thierry Cazenave, David Costa, Orlando Lopes, Raúl Manásevich, Paul Rabinowitz, Bernhard Ruf, Carlos Tomei

ISBN-10: 3764371498

ISBN-13: 9783764371494

ISBN-10: 3764374012

ISBN-13: 9783764374013

This quantity comprises learn and survey articles within the fields of nonlinear research and nonlinear differential equations, written via across the world complete researchers. The articles mirror the cutting-edge in those very important fields of present learn. the quantity is devoted to D.G. de Figueiredo, thereby honoring the $64000 contributions and lasting impression of a exceptional mathematician.

Show description

Read or Download Contributions to Nonlinear Analysis: A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday (Progress in Nonlinear Differential Equations and Their Applications) PDF

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Extra resources for Contributions to Nonlinear Analysis: A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday (Progress in Nonlinear Differential Equations and Their Applications)

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3. The semilinear Maxwell equations Here we report some results contained in [1] where a unitarian field theory, based on a semilinear perturbation of the Maxwell equations, has been introduced. We modify the usual Maxwell action in the empty space Sm (ϕ, A) = ∂A +∇ϕ ∂t 1 2 2 − |∇ × A| 2 dxdt in the following way: S= 1 2 2 ∂A 2 2 +∇ϕ − |∇ × A| + W |A| − ϕ2 ∂t dxdt (25) where W : R → R. 2 2 The argument of W is |A| − |ϕ| in order to make this expression invariant for the Poincar´e group and the equations consistent with special relativity.

1. (i) If v ∈ Lp + Lq , the following inequalities hold: v max ≤ v Lq (RN −Γv ) − 1, 1 1 1 + |Γv | τ v Lp (Γv ) Lp +Lq ≤ max v Lq (RN −Γv ) , v Lp (Γv ) pq . when τ = q−p (ii) Let {vn } ⊂ Lp +Lq and set Γn = {x ∈ Ω : |vn (x)| > 1}. Then {vn } is bounded in Lp + Lq if and only if the sequences vn Lq (RN −Γn ) + vn Lp (Γn ) and {|Γn |} are bounded. (iii) f is a bounded map from Lp + Lq into Lp/p−1 ∩ Lq/q−1 . 56 V. R. M. 2. 1 we have L2 ⊂ Lp + Lq when 2 < p < 2∗ < q. Then, by the Sobolev inequality, we get the continuous embedding D1,2 (RN ) ⊂ Lp + Lq .

Existence of Solutions In this section, we will show the existence of a positive solution for (Pλ ). We divide this section in subsections considering different situations involving the geometry of the function q(x) at infinity. 1. First Case: Equality at Infinity In this subsection, we show our first result considering the case where the function q is equal to a constant at infinity. The next proposition establishes an important inequality involving the minimax level c∞ of I∞ . 1 Let {un } be a (P S)d sequence for Iλ converging weakly to 0 in W 1,p(x) (IRN ).

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Contributions to Nonlinear Analysis: A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday (Progress in Nonlinear Differential Equations and Their Applications) by Thierry Cazenave, David Costa, Orlando Lopes, Raúl Manásevich, Paul Rabinowitz, Bernhard Ruf, Carlos Tomei


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