Nodal ground state solution to a biharmonic equation via dual method

Abstract

Using dual method we establish the existence of nodal ground state solution for the following class of problemswhere ∆ 2 is the biharmonic operator, B = ∆ or B = ∂ ∂ν and f is a C 1 − function having subcritical growth. (2010): 35J20, 35J65 Mathematics Subject Classifications

Existence of solution for a class of elliptic problems in exterior domain with discontinuous nonlinearity

“…If u is a critical point of J p 0 ;d with u AE 6 0; then J p 0 ;d ðuÞ ! 2c p 0 ;d .Proof The proof follows with the same type of arguments found in[4, Section 4] or[11, Theorem 2.4]. h…”

Multiple solutions for a problem with discontinuous nonlinearity

“…Proof The proof follows with the same type of arguments found in [10,Section 4] or [11,Theorem 2.4].…”

A study of biharmonic equation involving nonlocal terms and critical Sobolev exponent

“…Proof. Suppose that ground state solution of (1.2) is denoted by T ∈ H 2 0 (R N ) and such solution exists (see [2] and references therein). Assume that sT is the projection of T on N α , that is, s = s(T ) > 0 is the unique real number such that sT ∈ N α .…”