Two sequences of solutions for indefinitesuperlinear-sublinear elliptic equationswith nonlinear boundary conditions

Ryuji Kajikiya; Daisuke Naimen

doi:10.3934/cpaa.2014.13.1593

Article Contents

2014, Volume 13, Issue 4: 1593-1612. Doi: 10.3934/cpaa.2014.13.1593

This issue Previous Article Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data Next Article Global existence of strong solutions for $2$-dimensional Navier-Stokes equations on exterior domains with growing data at infinity

Two sequences of solutions for indefinite superlinear-sublinear elliptic equations with nonlinear boundary conditions

Ryuji Kajikiya^1, and
Daisuke Naimen^2,

1.
Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502
2.
Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto Sumiyoshi-ku, Osaka-shi, Osaka, 558-8585

Received: October 2013

Revised: January 2014

Published: July 2015

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Abstract

In this paper, we study semilinear elliptic equations with nonlinear Neumann boundary conditions. We prove the existence of a sequence of solutions converging to zero if the nonlinear term is locally sublinear and the existence of a sequence of solutions diverging to infinity if the nonlinear term is locally superlinear.

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Mathematics Subject Classification: Primary: 35J20; Secondary: 35J25, 35J66.

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