Ground States for a Class of Generalized Quasilinear Schrödinger Equations in $${\mathbb {R}}^N$$RN
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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
Existence of nontrivial solutions for generalized quasilinear Schrödinger equations with critical or supercritical growths
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DOI: 10.1016/s0252-9602(17)30113-3
Abstract: Abstract In this paper, we study the following generalized quasilinear Schrodinger equations with critical or supercritical growths - div ( g 2 ( u ) ∇ u ) + g ( u ) g ′… read more here.
Keywords: critical supercritical; nontrivial solutions; equations critical; generalized quasilinear ... See more keywords
Multiplicity and existence of solutions for generalized quasilinear Schrödinger equations with sign-changing potentials
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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