Ground State Solutions for a Quasilinear Schrödinger Equation
Sign Up to like & getrecommendations! Published in 2017 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-016-0816-3
Abstract: In this paper, we study the following quasilinear Schrödinger equation of the form $$\begin{aligned} -\Delta u+V(x)u-\Delta (u^{2})u= g(x,u),~~~ x\in \mathbb {R}^N \end{aligned}$$-Δu+V(x)u-Δ(u2)u=g(x,u),x∈RNwhere V and g are 1-periodic in $$x_{1},\ldots ,x_{N}$$x1,…,xN, and g is a superlinear… read more here.
Keywords: dinger equation; state solutions; quasilinear schr; ground state ... See more keywords
Ground States for a Class of Generalized Quasilinear Schrödinger Equations in $${\mathbb {R}}^N$$RN
Sign Up to like & getrecommendations! Published in 2017 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-017-0990-y
Abstract: In this paper, we study the following generalized quasilinear Schrödinger equation: $$\begin{aligned} -\text {div}(g^2(u)\nabla u)+g(u)g'(u)|\nabla u|^2+V(x)u=f(x,u),\,\, x\in {\mathbb {R}}^N, \end{aligned}$$-div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=f(x,u),x∈RN, where $$N\ge 3$$N≥3, $$2^*=\frac{2N}{N-2}$$2∗=2NN-2, $$g\in \mathcal {C}^1({\mathbb {R}},{\mathbb {R}}^{+})$$g∈C1(R,R+), V(x) is 1-periodic or a bounded… read more here.
Keywords: quasilinear schr; ground states; generalized quasilinear; schr dinger ... See more keywords
Standing waves for quasilinear Schrödinger equations with indefinite potentials
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2018.05.024
Abstract: Abstract We consider quasilinear Schrodinger equations in R N of the form − Δ u + V ( x ) u − u Δ ( u 2 ) = g ( u ) , where… read more here.
Keywords: dinger equations; waves quasilinear; equations indefinite; quasilinear schr ... See more keywords
Solutions for a quasilinear Schrödinger equation: Subcritical and critical cases
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0142706
Abstract: In this paper, we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving nonlinearity with subcritical and critical growth. To apply the variational method and circumvent the “lack of compactness” of the… read more here.
Keywords: solutions quasilinear; quasilinear schr; differ equations; subcritical critical ... See more keywords
The first eigenvalue for a quasilinear Schrödinger operator and its application
Sign Up to like & getrecommendations! Published in 2018 at "Applicable Analysis"
DOI: 10.1080/00036811.2016.1274026
Abstract: In this paper, we study the first eigenvalue for a quasilinear Schrödinger operator, which is greater than the first eigenvalue of the usual laplacian operator. As an application we treat a quasilinear resonance problem involving… read more here.
Keywords: first eigenvalue; eigenvalue quasilinear; quasilinear schr; dinger operator ... See more keywords
Infinitely many solutions for a class of quasilinear Schrödinger equations involving sign-changing weight functions
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2017.1422726
Abstract: ABSTRACT Using a change of variables and the constrained critical point theory, we first prove the existence and multiplicity of solutions for a class of quasilinear Schrödinger equations. Next, we consider a quasilinear equation related… read more here.
Keywords: dinger equations; class quasilinear; solutions class; sign changing ... See more keywords
Concentrating ground state solutions for quasilinear Schrödinger equations with steep potential well
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2019.1707814
Abstract: We are concerned with the following quasilinear Schrödinger equations (1) where , are parameters, V and f are nonnegative continuous functions, is a positive bounded function. By using variational methods, we study the existence of… read more here.
Keywords: dinger equations; state solutions; quasilinear schr; ground state ... See more keywords
Nonexistence of solutions for quasilinear Schrödinger equation in ℝN
Sign Up to like & getrecommendations! Published in 2020 at "Applicable Analysis"
DOI: 10.1080/00036811.2020.1854231
Abstract: In this paper, we study the nonexistence of solutions to the quasilinear Schrodinger equations: (1) − Δ p u + V ( x ) | u | p − 2 u − Δ p (… read more here.
Keywords: nonexistence solutions; dinger equation; quasilinear schr; solutions quasilinear ... See more keywords
Positive solutions for quasilinear Schrödinger equations with superlinear term
Sign Up to like & getrecommendations! Published in 2019 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2019.1636791
Abstract: ABSTRACT In this paper, we study the following quasilinear Schrödinger equation where , is a given potential, g is a even function with for all . The nonlinearity satisfies superlinear growth at infinity. We get… read more here.
Keywords: dinger equations; positive solutions; quasilinear schr; solutions quasilinear ... See more keywords
Nonexistence of stable solutions for quasilinear Schrödinger equation
Sign Up to like & getrecommendations! Published in 2018 at "Boundary Value Problems"
DOI: 10.1186/s13661-018-1087-7
Abstract: AbstractIn this paper, we study the nonexistence of stable solutions for the quasilinear Schrödinger equation 0.1−Δu−[Δ(1+u2)1/2]u2(1+u2)1/2=h(x)|u|q−1u,x∈RN,$$ -\Delta u- \bigl[\Delta\bigl(1+u^{2}\bigr)^{1/2} \bigr]\frac{ u}{2(1+u^{2})^{1/2}}=h(x) \vert u \vert ^{q-1}u,\quad x\in R^{N}, $$ where N≥3$N\ge3$, q≥5/2$q\ge5/2$ and the function h(x)$h(x)$… read more here.
Keywords: dinger equation; nonexistence stable; quasilinear schr; solutions quasilinear ... See more keywords
Multiplicity and existence of solutions for generalized quasilinear Schrödinger equations with sign-changing potentials
Sign Up to like & getrecommendations! Published in 2020 at "Boundary Value Problems"
DOI: 10.1186/s13661-020-01369-6
Abstract: We consider a class of generalized quasilinear Schrödinger equations − div ( l 2 ( u ) ∇ u ) + l ( u ) l ′ ( u ) | ∇ u | 2… read more here.
Keywords: dinger equations; dinger; generalized quasilinear; sign changing ... See more keywords