In this paper, we establish existence and multiplicity of solutions for the following class of quasilinear field equation
where is a singular function and is a positive continuous function.
Keywords: Nonlinear elliptic equations, variational methods
@article{COCV_2018__24_3_1231_0, author = {Alves, Claudianor O. and dos Santos, Alan C.B.}, title = {Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on {\ensuremath{\mathbb{R}}\protect\textsuperscript{N}}}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1231--1248}, publisher = {EDP-Sciences}, volume = {24}, number = {3}, year = {2018}, doi = {10.1051/cocv/2017045}, zbl = {1410.35049}, mrnumber = {3877200}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017045/} }
TY - JOUR AU - Alves, Claudianor O. AU - dos Santos, Alan C.B. TI - Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on ℝN JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1231 EP - 1248 VL - 24 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017045/ DO - 10.1051/cocv/2017045 LA - en ID - COCV_2018__24_3_1231_0 ER -
%0 Journal Article %A Alves, Claudianor O. %A dos Santos, Alan C.B. %T Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on ℝN %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1231-1248 %V 24 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017045/ %R 10.1051/cocv/2017045 %G en %F COCV_2018__24_3_1231_0
Alves, Claudianor O.; dos Santos, Alan C.B. Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on ℝN. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 3, pp. 1231-1248. doi : 10.1051/cocv/2017045. http://archive.numdam.org/articles/10.1051/cocv/2017045/
[1] Existence, multiplicity and concentration of bound states for a quasilinear elliptic field equation. Calc. Var. 12 (2001) 223–258 | DOI | MR | Zbl
, and ,[2] Semiclassical limit for a quasilinear elliptic field equation: One-Peak and Multi-Peak solutions. Adv. Differ. Equ. 6 (2001) 385–418 | MR | Zbl
, and ,[3] Existence and multiplicity results for some superlinear elliptic problems on ℝN. Commun. Partial Differ. Equ. 20 (1995) 1725–1741 | DOI | MR | Zbl
and ,[4] Existence and multiplicity results for some superlinear elliptic problems on ℝN. Commun. Partial Differ. Equ. 20 (1995) 1725–1741 | DOI | MR | Zbl
and ,[5] Multiple positive solutions for a nonlinear Schrödinger equation. Z. Angew. Math. Phys. 51 (2000) 366–384 | DOI | MR | Zbl
and ,[6] Solitons in several space dimensions: Derrick’s problem and infinitely solutions.Arch. Rational Mech. Anal. 154 (2000) 297–324 | DOI | MR | Zbl
, , and ,[7] Remarks on topological solitons. Topol. Methods Nonlinear Anal. 7 (1996) 349–367 | DOI | MR | Zbl
, and ,[8] Soliton like solutions of a Lorentz invariant equation in dimension 3. Rev. Math. Phys. 6 (1998) 315–344 | DOI | MR | Zbl
, and ,[9] An eigenvalue problem for a quasilinear elliptic field equation. J. Differ. Equ. 184 (2002) 299–320 | DOI | MR | Zbl
, and ,[10] An eigenvalue problem for a quasilinear elliptic field equation on ℝN. Topol. Methods Nonl. Anal. 17 (2001) 191–211 | MR | Zbl
, and ,[11] Solitons and electromagnetic field. Math. Z. 232 (1999) 349–367 | DOI | MR | Zbl
, , and ,[12] On a class of elliptic systems in ℝN. Electron. J. Differ. Equ. 1994 (1994) 1–14 | MR | Zbl
,[13] Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle. Electron. J. Differ. Equ. 2000 (2000) 1–40 | MR | Zbl
,[14] Semiclassical states for a class of nonlinear elliptic field equations. Asymptot. Anal. 37 (2004) 109–141 | MR | Zbl
,[15] Some results on a nonlinear elliptic field equation involving the p-Laplacian. Nonlinear Anal. 47 (2001) 5979–5989 | DOI | MR | Zbl
,[16] Existence and concentration of local mountain-passes for a nonlinear elliptic field equation in the semiclassical limit. Topol. Methods Nonlinear Anal. 17 (2001) 239–276 | DOI | MR | Zbl
,[17] Discreteness of spectrum for the Schrödinger operators on manifolds of bounded geometry, in: The Mazya Anniversary Collection, Operator Theory: Advances and Applications, vol 110. Birkhäuser, Basel (1999) 185–226 | MR | Zbl
and ,[18] Homoclinic orbits for a class of Hamiltonian systems. Differ. Integral Equ. 5 (1992) 1115–1120 | MR | Zbl
and ,[19] Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in ℝN. Eletron. J. Differ. Equ. 2005 (2005) | MR | Zbl
,[20] New nonlinear equations with soliton-like solutions. Lett. Math. Phys. 57 (2001) 161–173 | DOI | MR | Zbl
,[21] On a class of nonlinear Schrödinger equations. Z. Angew Math. Phys. 43 (1992) 270–291 | DOI | MR | Zbl
,Cited by Sources: