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This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems \[-\Delta v=\lambda h(x, v)\ \ \text{in}\ \Omega,\ \ \ v=0\ \ \text{on}\ \partial\Omega, \] where $\Omega=\{x\in \mathbb{R}^N: r_1<|x|<r_2\}$ with $0<r_1<r_2,\ N\geq2$. The nonlinear term is continuous and satisfies $h(x, 0)=h(x, s_1(x))=h(x, s_2(x))=0$ for suitable positive, concave function $s_1$ and negative, convex function $s_2$, as well as $sh(x, s)>0$ for $s\in\mathbb{R}\setminus\{0, s_1(x), s_2(x)\}$. Moreover, we give the intervals for the parameter $\lambda$ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.
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참고문헌 (19)
참고문헌 신청
A Ambrosetti / 1980 / Positive solutions of asymptotically linear elliptic eigenvalue problems / Journal of Mathematical Analysis and Applications 73(2):411~422
Guowei Dai / 2016 / Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros / Discrete and Continuous Dynamical Systems 36(10):5323~5345
Guowei Dai / 2012 / Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian / Journal of Differential Equations 252(3):2448~2468
Guowei Dai / 2013 / Bifurcation from infinity and nodal solutions of quasilinear problems without the signum condition / Journal of Mathematical Analysis and Applications 397(1):119~123
E. Dancer / 1974 / On the structure of solutions of non-linear eigenvalue problems / Indiana University Mathematics Journal 23(11):1069~1076
Guowei Dai / 2016 / Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros / Discrete and Continuous Dynamical Systems 36(10):5323~5345
Guowei Dai / 2012 / Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian / Journal of Differential Equations 252(3):2448~2468
Guowei Dai / 2013 / Bifurcation from infinity and nodal solutions of quasilinear problems without the signum condition / Journal of Mathematical Analysis and Applications 397(1):119~123
E. Dancer / 1974 / On the structure of solutions of non-linear eigenvalue problems / Indiana University Mathematics Journal 23(11):1069~1076
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