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Aims. The purpose of this paper is to detect and investigate the nature oflong-term radial velocity (RV) variations of K-type giants and to confirmplanetary companions around the stars.  Methods. We have conducted two planet search programs by precise RVmeasurement using the 1.8 m telescope at Bohyunsan Optical AstronomyObservatory (BOAO) and the 1.88 m telescope at Okayama AstrophysicalObservatory (OAO). The BOAO program searches for planets around 55 early Kgiants. The OAO program is looking for 190 G-K type giants.  Results. In this paper, we report the detection of long-period RV variationsof three K giant stars, HD 40956, HD 111591, and HD 113996. We investigated thecause of the observed RV variations and conclude the substellar companions aremost likely the cause of the RV variations. The orbital analyses yield P =578.6 $\pm$ 3.3 d, $m$ sin $i$ = 2.7 $\pm$ 0.6 $M_{\rm{J}}$, $a$ = 1.4 $\pm$0.1 AU for HD 40956; P = 1056.4 $\pm$ 14.3 d, $m$ sin $i$ = 4.4 $\pm$ 0.4$M_{\rm{J}}$, $a$ = 2.5 $\pm$ 0.1 AU for HD 111591; P = 610.2 $\pm$ 3.8 d, $m$sin $i$ = 6.3 $\pm$ 1.0 $M_{\rm{J}}$, $a$ = 1.6 $\pm$ 0.1 AU for HD 113996.

Detection of planet candidates around K giants, HD 40956, HD 111591, and HD 113996