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Title of Journal: Calc Var

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Abbravation: Calculus of Variations and Partial Differential Equations

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Springer-Verlag

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10.1007/s11192-015-1698-z

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1432-0835

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Solitary waves for a class of quasilinear Schrödin

Authors: João Marcos do Ó Uberlandio Severo
Publish Date: 2009/11/13
Volume: 38, Issue: 3-4, Pages: 275-315
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Abstract

In this paper we prove the existence and concentration behavior of positive ground state solutions for quasilinear Schrödinger equations of the form −ε 2Δu + Vzu − ε 2 Δu 2u = hu in the whole twodimension space where ε is a small positive parameter and V is a continuous potential uniformly positive The main feature of this paper is that the nonlinear term hu is allowed to enjoy the critical exponential growth with respect to the Trudinger–Moser inequality and also the presence of the second order nonhomogeneous term Δu 2u which prevents us to work in a classical Sobolev space Using a version of the Trudinger–Moser inequality a penalization technique and mountainpass arguments in a nonstandard Orlicz space we establish the existence of solutions that concentrate near a local minimum of V

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  2. Fractional Poincaré inequality with finite total Q -curvature
  3. Thick clusters for the radially symmetric nonlinear Schrödinger equation
  4. On elliptic systems with Sobolev critical growth
  5. Critical points for functionals with quasilinear singular Euler–Lagrange equations
  6. Duality for rectified cost functions
  7. An approach to minimization under a constraint: the added mass technique
  8. Single-point condensation phenomena for a four-dimensional biharmonic Ren–Wei problem
  9. Uniqueness and nondegeneracy of positive radial solutions of $$\mathbf {div\,{\varvec{(}}{\varvec{\rho }} \nabla u{\varvec{)}} +{\varvec{\rho }}{\varvec{(}}-gu+hu^p{\varvec{)}}=0}$$
  10. Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds
  11. Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators
  12. Sharp energy estimates for nonlinear fractional diffusion equations
  13. On Newton equations which are totally integrable at infinity
  14. Energy asymptotics for Type II superconductors
  15. Regularity for fully nonlinear nonlocal parabolic equations with rough kernels
  16. Singular points of Hölder asymptotically optimally doubling measures
  17. Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
  18. Cahn–Hilliard–Navier–Stokes systems with moving contact lines
  19. A mean field type flow part I: compactness of solutions to a perturbed mean field type equation
  20. Boundary value problems for Willmore curves in $$\mathbb {R}^2$$
  21. Fractional eigenvalues
  22. On a quasilinear system involving the operator curl
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  24. Moser–Trudinger inequalities of vector bundle over a compact Riemannian manifold of dimension 2
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