Branch continuation inside the essential spectrum for the nonlinear Schrodinger equation

被引:11
|
作者
Evequoz, Gilles [1 ]
Weth, Tobias [1 ]
机构
[1] Goethe Univ Frankfurt, Inst Mathemat, Robert Mayer Str 10, D-60629 Frankfurt, Germany
关键词
Nonlinear Schrodinger equation; Nonlinear Helmholtz equation; Global branch of solutions; A priori bounds; Leray-Schauder fixed-point index; SEMILINEAR ELLIPTIC PROBLEMS; SCALAR FIELD-EQUATIONS; POSITIVE SOLUTIONS; BIFURCATION; EXISTENCE; THEOREMS;
D O I
10.1007/s11784-016-0362-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the nonlinear stationary Schrodinger equation -Delta u - lambda u = Q(x)vertical bar u vertical bar(p-2) u, in R-N in the case where N >= 3, p is a superlinear, subcritical exponent, Q is a bounded, nonnegative and nontrivial weight function with compact support in R-N and lambda is an element of R is a parameter. Under further restrictions either on the exponent p or on the shape of Q, we establish the existence of a continuous branch C of nontrivial solutions to this equation which intersects {lambda} x L-s(R-N) for every lambda is an element of (-infinity, lambda(Q)) and s > 2N/N-1. Here, lambda(Q) > 0 is an explicit positive constant which only depends on N and diam(supp Q). In particular, the set of values lambda along the branch enters the essential spectrum of the operator -Delta.
引用
收藏
页码:475 / 502
页数:28
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