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Table Of Integrals Series And Products

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Thank you very much for reading methods of modern mathematical physics. Maybe you have knowledge that, people have look numerous times for their favorite novels like this methods of modern mathematical physics, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their desktop computer. methods of modern mathematical physics is available in our digital library an online access to it is set as public so you can download it instantly. Our books collection saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the methods of modern mathematical physics is universally compatible with any devices to read.

Methods Of Modern Mathematical Physics

Preliminaries.- Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.

Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States

Preface.- Preface to the 2nd edition.- Notational conventions.- 1 Preliminary general material.- I Steady-state problems.- 2 Pseudomonotone or weakly continuous mappings.- 3 Accretive mappings.- 4 Potential problems: smooth case.- 5 Nonsmooth problems variational inequalities.- 6. Systems of equations: particular examples.- II Evolution problems.- 7 Special auxiliary tools.- 8 Evolution by pseudomonotone or weakly continuous mappings.- 9 Evolution governed by accretive mappings.- 10 Evolution governed by certain set-valued mappings.- 11 Doubly-nonlinear problems.- 12 Systems of equations: particular examples.- References.- Index.

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Nonlinear partial differential equations with applications

We study the semilinear elliptic PDE in RN The nonlinearity ƒ will be superlinear and subcritical We prove the existence 0f a positive solution under various hypotheses on b If and ƒ is odd in u,

Existence and multiplicity results for some superlinear elliptic problems on RN

We investigate nonlinear Schrodinger equations like the model equation \[ -\Delta u +V_\lambda (x) u =| u |^{p -2} u\,, \quad x\in {\mathbb R}^N\,, \ 2 0. If λ → ∞ the infimum of the essential spectrum of -Δ + Vλ in L2(ℝN) converges towards ∞ and more and more eigenvalues appear below the essential spectrum. We show that as λ→∞ more and more solutions of the nonlinear Schrodinger equation exist. The solutions lie in H1(ℝN) and are localized near the bottom of the potential well, but not near local minima of the potential. We also investigate the decay rate of the solutions as |x|→∞ as well as their behaviour as λ→∞.

Nonlinear schrödinger equations with steep potential well

Critical point theory for asymptotically quadratic functionals and applications to problems with resonance

The paper is concerned with the local and global bifurcation structure of positive solutions ${u,v\in H^1_0(\Omega)}$ of the system

$$\left\{\begin{array}{lll}-\Delta u + u = \mu_1u^3+\beta v^2u &\quad\text{in $\Omega$}\\-\Delta v + v = \mu_2v^3+\beta u^2v &\quad\text{in $\Omega$}\nonumber\end{array}\right.$$

of nonlinear Schrodinger (or Gross-Pitaevskii) type equations in ${\Omega\subset\mathbb {R}^N}$, N ≤ 3. The system arises in nonlinear optics and in the Hartree–Fock theory for a double condensate. Local and global bifurcations in terms of the nonlinear coupling parameter β of the system are investigated by using spectral analysis and by establishing a new Liouville type theorem for nonlinear elliptic systems which provides a-priori bounds of solution branches. If the domain is radial, possibly unbounded, then we also control the nodal structure of a certain weighted difference of the components of the solutions along the bifurcating branches.

/pdf/a-liouville-theorem-a-priori-bounds-and-bifurcating-branches-8lbqjjdejp.pdf

A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system

We study the semilinear elliptic equation -Delta u=lambdau(q-2)u+muu(p-2)u in an open bounded domain Omega subset of R(N) with Dirichlet boundary conditions; here 1 0 and mu is an element of R arbitrary there exists a sequence (upsilon(k)) of solutions with negative energy converging to 0 as k --> infinity. Moreover, for mu > 0 and lambda arbitrary there exists a sequence of solutions with unbounded energy. This answers a question of Ambrosetti, Brezis and Cerami. The main ingredient is a new critical point theorem, which guarantees the existence of infinitely many critical values of an even functional in a bounded range. We can also treat strongly indefinite functionals and obtain similar results for first-order Hamiltonian systems.

/pdf/on-an-elliptic-equation-with-concave-and-convex-3iz8kkb44k.pdf

Thomas Bartsch

Papers

Existence and multiplicity results for some superlinear elliptic problems on RN

Nonlinear schrödinger equations with steep potential well

Critical point theory for asymptotically quadratic functionals and applications to problems with resonance

A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system

On an elliptic equation with concave and convex nonlinearities