NODAL SOLUTIONS OF 2-D CRITICAL NONLINEAR SCHRODINGER EQUATIONS WITH POTENTIALS VANISHING AT INFINITY

作者：Fei Mingwen; Yin Huicheng^*

来源：Discrete and Continuous Dynamical Systems, 2015, 35(7): 2921-2948.

DOI：10.3934/dcds.2015.35.2921

• Nonlinear Schrodinger equation
• critical exponent
• nodal solution
• multi-peak
• concentration-compactness

We will focus on the existence and concentration of nodal solutions to the following critical nonlinear Schrodinger equations in R-2 -epsilon(2)Delta u(epsilon) + V (x)u(epsilon) - K (x)vertical bar u epsilon vertical bar(p -2)u(epsilon)e(alpha 0)vertical bar u(epsilon)vertical bar(2), u(epsilon) is an element of H-1 (R-2), where p > 2, alpha(0) > 0, V (x), K (x) > 0, and epsilon > 0 is a small constant. For the positive potential V (x) which decays at infinity like (1 + vertical bar x vertical bar)(-alpha) with 0 < alpha <= 2, we will show that a nodal solution with one positive and one negative peaks exists, and concentrates around local minimum points of the related ground energy function G (xi) of the Schrodinger equation -Delta u + V (xi)u = K (xi)vertical bar u vertical bar(p) - (2)ue(alpha 0)vertical bar u vertical bar(2).

• 出版日期2015-7
• 单位南京大学