Entire blow-up solutions for a quasilinear p-Laplacian Schrödinger equation with a non-square diffusion term

Abstract In this paper, we study the entire blow-up solutions for a quasilinear p -Laplacian Schrodinger elliptic equation with a non-square diffusion term. By using the dual approach and some new iterative techniques, the difficulty due to the non-square diffusion term and the p -Laplacian operator is overcome and the nonexistence and existence of entire blow-up solutions are established.

[1]  F. Zhou,et al.  Infinitely many small solutions for a modified nonlinear Schrödinger equations , 2014 .

[2]  Bo Sang,et al.  Limit cycle bifurcated from a center in a three dimensional system , 2016 .

[3]  Yujun Cui,et al.  Uniqueness of solution for boundary value problems for fractional differential equations , 2016, Appl. Math. Lett..

[4]  Xinguang Zhang,et al.  Exact Iterative Solution for an Abstract Fractional Dynamic System Model for Bioprocess , 2017 .

[5]  Yujun Cui,et al.  Monotone iterative technique for $(k, n-k)$ conjugate boundary value problems , 2015 .

[6]  Xinguang Zhang,et al.  A necessary and sufficient condition for the existence of large solutions to 'mixed' type elliptic systems , 2012, Appl. Math. Lett..

[7]  Tatsuya Watanabe,et al.  Uniqueness of the ground state solutions of quasilinear Schrödinger equations , 2012 .

[8]  Alan Weinstein,et al.  Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential , 1986 .

[9]  Yumei Zou,et al.  Existence Results and the Monotone Iterative Technique for Nonlinear Fractional Differential Systems with Coupled Four-Point Boundary Value Problems , 2014 .

[10]  Susumu Kurihara,et al.  Large-Amplitude Quasi-Solitons in Superfluid Films , 1981 .

[11]  G. Quispel,et al.  Equation of motion for the Heisenberg spin chain , 1981 .

[12]  Alan V. Lair,et al.  Large solutions of semilinear elliptic problems , 1999 .

[13]  Xinguang Zhang,et al.  The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term , 2010 .

[14]  Yumei Zou,et al.  Monotone iterative method for differential systems with coupled integral boundary value problems , 2013 .

[15]  Jaeyoung Byeon,et al.  Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations , 2002 .

[16]  Rainer W. Hasse,et al.  A general method for the solution of nonlinear soliton and kink Schrödinger equations , 1980 .

[17]  Alan V. Lair,et al.  Large solutions of semilinear elliptic equations under the Keller–Osserman condition , 2007 .

[18]  Caisheng Chen.  Multiple solutions for a class of quasilinear Schrödinger equations in ℝN , 2015 .

[19]  Alan V. Lair,et al.  Large solutions of sublinear elliptic equations , 2000 .

[20]  Lou Caccetta,et al.  Entire large solutions for a class of Schrödinger systems with a nonlinear random operator , 2015 .

[21]  Haitao Yang.  On the existence and asymptotic behavior of large solutions for a semilinear elliptic problem in $R^n$ , 2004 .

[22]  V. Makhankov,et al.  Non-linear effects in quasi-one-dimensional models of condensed matter theory , 1984 .

[23]  Jiaquan Liu,et al.  Soliton solutions for quasilinear Schrödinger equations, II , 2003 .

[24]  Yonghong Wu,et al.  The entire large solutions for a quasilinear Schrödinger elliptic equation by the dual approach , 2016, Appl. Math. Lett..

[25]  Pierre-Louis Lions,et al.  Nonlinear scalar field equations, I existence of a ground state , 1983 .