Elliptic problem driven by different types of nonlinearitiesChoudhuri, Debajyoti (Avtor) Repovš, Dušan (Avtor) fractional Laplacianground state solutionsingularityIn this paper we establish the existence and multiplicity of nontrivial solutions to the following problem: $$(-\Delta )^{\frac{1}{2}}u+u+\bigl(\ln \vert \cdot \vert \ast \vert u \vert ^{2}\bigr) = f(u)+\mu \vert u \vert ^{- \gamma -1}u,\quad \text{in }\mathbb{R},$$ where $\mu > 0$, $(\ast)$ is the convolution operation between two functions, $0<\gamma <1$, $f$ is a function with a certain type of growth. We prove the existence of a nontrivial solution at a certain mountain pass level and another ground state solution when the nonlinearity $f$ is of exponential critical growth.20212021-10-25 11:56:57Članek v reviji132413sl