@article{Shen2023, 
author = {Wenguo Shen},
title = {Bifurcation and one-sign solutions for semilinear elliptic problems in              R              N},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {5},
pages = {10453-10467},
keywords = {unilateral global bifurcation, one-sign solutions, semilinear elliptic problems},
url = {https://www.sciopen.com/article/10.3934/math.2023530},
doi = {10.3934/math.2023530},
abstract = {In this work, we study the existence of one-sign solutions without signum condition for the following problem:                                 {                                                    −                Δ                u                =                λ                a                (                x                )                f                (                u                )                ,                                                x                ∈                                                      R                                                        N                                                  ,                                                                                                                                u                (                x                )                →                0                ,                                                                                                                                                                                                                                                                                                                                                                                                                      a                    s                                                                                                    |                                x                                  |                                →                +                ∞                ,                                                                                                                                                                  where    N  ≥  3,    λ is a real parameter and    a  ∈      C          l      o      c              α        (            R              N        ,      R    ) for some    α  ∈  (  0  ,  1  ) is a weighted function,    f  ∈      C          α        (      R    ,      R    ), and there exist two constants        s          2        <  0  <      s          1        , such that    f  (      s          1        )  =  f  (      s          2        )  =  f  (  0  )  =  0 and    s  f  (  s  )  >  0 for    s  ∈      R    ∖  {      s          1        ,  0  ,      s          2        }  . Furthermore, we consider the exact multiplicity of one-sign solutions for above problem under more strict hypotheses. We use bifurcation techniques and the approximation of connected components to prove our main results.}
}